CoreFlows/Models/src/IsothermalTwoFluid.cxx

   1 /*
   2  * IsothermalTwoFluid.cxx
   3  *
   4  *  Created on: Sep 16, 2014
   5  *      Author: tn236279
   6  */
   7
   8 #include "IsothermalTwoFluid.hxx"
   9
  10 using namespace std;
  11
  12 IsothermalTwoFluid::IsothermalTwoFluid(pressureEstimate pEstimate, int dim){
  13         _Ndim=dim;
  14         _nVar=2*(_Ndim+1);
  15         _nbPhases = 2;
  16         _dragCoeffs=vector<double>(2,0);
  17         _fluides.resize(2);
  18         if (pEstimate==around1bar300K)//EOS at 1 bar and 300K
  19         {
  20                 cout<<"Fluid is air-water mixture around 1 bar and 300 K (27°C)"<<endl;
  21                 *_runLogFile<<"Fluid is air-water mixture around 1 bar and 300 K (27°C)"<<endl;
  22                 _Temperature=300;//Constant temperature of the model
  23                 _internalEnergy1=2.22e5;//nitrogen internal energy at 1bar, 300K
  24                 _internalEnergy2=1.12e5;//water internal energy at 1 bar, 300K
  25                 _fluides[0] = new StiffenedGas(1.4,743,_Temperature,_internalEnergy1);  //ideal gas law for nitrogen at pressure 1 bar and temperature 27°C, c_v=743
  26                 _fluides[1] = new StiffenedGas(996,1e5,_Temperature,_internalEnergy2,1501,4130);  //stiffened gas law for water at pressure 1 bar and temperature 27°C
  27         }
  28         else//EOS at 155 bars and 618K
  29         {
  30                 cout<<"Fluid is water-Gas mixture around saturation point 155 bars and 618 K (345°C)"<<endl;
  31                 *_runLogFile<<"Fluid is water-Gas mixture around saturation point 155 bars and 618 K (345°C)"<<endl;
  32                 _Temperature=618;//Constant temperature of the model
  33                 _internalEnergy1=2.44e6;//Gas internal energy at saturation at 155 bar
  34                 _internalEnergy2=1.6e6;//water internal energy at saturation at 155 bar
  35                 _fluides[0] = new StiffenedGas(102,1.55e7,_Temperature,_internalEnergy1, 433,3633);  //stiffened gas law for Gas at pressure 155 bar and temperature 345°C:
  36                 _fluides[1] = new StiffenedGas(594,1.55e7,_Temperature,_internalEnergy2, 621,3100);  //stiffened gas law for water at pressure 155 bar and temperature 345°C:
  37         }
  38         _intPressCoeff=1.5;
  39 }
  40
  41 void IsothermalTwoFluid::initialize(){
  42         cout<<"Initialising the isothermal two-fluid model"<<endl;
  43         *_runLogFile<<"Initialising the isothermal two-fluid model"<<endl;
  44
  45         _Uroe = new double[_nVar+1];
  46
  47         _guessalpha = _VV(0,0);
  48
  49         _gravite = vector<double>(_nVar,0);//Not to be confused with _GravityField3d (size _Ndim). _gravite (size _Nvar) is usefull for dealing with source term and implicitation of gravity vector
  50         for(int i=0; i<_Ndim; i++)
  51         {
  52                 _gravite[i+1]=_GravityField3d[i];
  53                 _gravite[i+1 +_Ndim+1]=_GravityField3d[i];
  54         }
  55         _GravityImplicitationMatrix = new PetscScalar[_nVar*_nVar];
  56
  57         if(_saveVelocity){
  58                 _Vitesse1=Field("Gas velocity",CELLS,_mesh,3);//Forcement en dimension 3 pour le posttraitement des lignes de courant
  59                 _Vitesse2=Field("Liquid velocity",CELLS,_mesh,3);//Forcement en dimension 3 pour le posttraitement des lignes de courant
  60         }
  61         if(_entropicCorrection)
  62                 _entropicShift=vector<double>(3,0);
  63
  64         ProblemFluid::initialize();
  65 }
  66
  67 void IsothermalTwoFluid::convectionState( const long &i, const long &j, const bool &IsBord){
  68         //sortie: WRoe en (alpha, p, u1, u2, dm1,dm2,dalpha1,dp)z
  69         //entree: _conservativeVars en (alpha1 rho1, alpha1 rho1 u1, alpha2 rho2, alpha2 rho2 u2)
  70
  71         // _l always inside the domain (index i)
  72         // _r is maybe the boundary cell (negative index)
  73         // _l and _r are primative vectors (alp, P, u1, u2)
  74
  75         _idm[0] = _nVar*i;
  76         for(int k=1; k<_nVar; k++)
  77                 _idm[k] = _idm[k-1] + 1;
  78         VecGetValues(_conservativeVars, _nVar, _idm, _Ui);
  79
  80         _idm[0] = _nVar*j;
  81         for(int k=1; k<_nVar; k++)
  82                 _idm[k] = _idm[k-1] + 1;
  83         if(IsBord)
  84                 VecGetValues(_Uext, _nVar, _idm, _Uj);
  85         else
  86                 VecGetValues(_conservativeVars, _nVar, _idm, _Uj);
  87         if(_verbose && _nbTimeStep%_freqSave ==0)
  88         {
  89                 cout<<"Convection Left state cell " << i<< ": "<<endl;
  90                 for(int k =0; k<_nVar; k++)
  91                         cout<< _Ui[k]<<endl;
  92                 cout<<"Convection Right state cell " << j<< ": "<<endl;
  93                 for(int k =0; k<_nVar; k++)
  94                         cout<< _Uj[k]<<endl;
  95         }
  96         //       if(_Ui[0]<-(_precision) || _Uj[0]<-(_precision) || _Ui[_Ndim+1]<-(_precision) || _Uj[_Ndim+1]<-(_precision))
  97         //      {
  98         //        cout<<"!!!!!!!!!!!!!!!!!!!!!!!! Masse partielle negative, arret de calcul!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"<<endl;
  99         //        cout<< "valeurs a gauche: "<<_Ui[0]<<", "<<_Ui[_Ndim+1]<<"valeurs a droite: "<<_Uj[0]<<", "<<_Uj[_Ndim+1]<<endl;
 100         //        throw CdmathException(" Masse partielle negative, arret de calcul");
 101         //      }
 102         //       else
 103         {
 104                 _Ui[0]=max(0.,_Ui[0]);// mass1 a gauche
 105                 _Uj[0]=max(0.,_Uj[0]);// mass1 a droite
 106                 _Ui[_Ndim+1]=max(0.,_Ui[_Ndim+1]);// mass2 a gauche
 107                 _Uj[_Ndim+1]=max(0.,_Uj[_Ndim+1]);// mass2 a droite
 108         }
 109
 110         PetscScalar ri1, ri2, rj1, rj2, xi, xj;
 111         _idm[0] = _nVar*i;
 112         for(int k=1; k<_nVar; k++)
 113                 _idm[k] = _idm[k-1] + 1;
 114         VecGetValues(_primitiveVars, _nVar, _idm, _l);
 115
 116         if(_verbose && _nbTimeStep%_freqSave ==0)
 117         {
 118                 cout<<"Etat de Roe, etat primitif gauche: "<<endl;
 119                 for(int i =0; i<_nVar; i++)
 120                         cout<< _l[i]<<endl;
 121         }
 122
 123         // boundary : compute the _r
 124         if(IsBord)
 125         {
 126                 _guessalpha=_l[0];
 127                 consToPrim(_Uj, _r);
 128         }
 129         // inside the domain : extract from the primative vector
 130         else
 131         {
 132                 _idm[0] = _nVar*j;
 133                 for(int k=1; k<_nVar; k++)
 134                         _idm[k] = _idm[k-1] + 1;
 135                 VecGetValues(_primitiveVars, _nVar, _idm, _r);
 136         }
 137
 138         if(_verbose && _nbTimeStep%_freqSave ==0)
 139         {
 140                 cout<<"Etat de Roe, etat primitif droite: "<<endl;
 141                 for(int i =0; i<_nVar; i++)
 142                         cout<< _r[i]<<endl;
 143         }
 144
 145         // Using Toumi linearisation (read in the article of Toumi) : alpha^{Roe}_l
 146         if(2-_l[0]-_r[0] > _precision)
 147                 _Uroe[0] = 1- 2*(1-_l[0])*(1-_r[0])/(2-_l[0]-_r[0]);
 148         // Using an average : (alp_l + alp_r)/2 : suggestion of Michael (no theory)
 149         else
 150                 _Uroe[0] = (_l[0]+_r[0])/2;
 151         // Pressure is computed as function of alp and P_l, P_r (Toumi article)
 152         if(_l[0]+_r[0] > _precision)
 153                 _Uroe[1] = (_l[1]*_l[0]+_r[1]*_r[0])/(_l[0]+_r[0]);
 154         else
 155                 _Uroe[1] = (_l[1]*(1-_l[0])+_r[1]*(1-_r[0]))/(2-_l[0]-_r[0]);
 156         // i :left, j : right (U is normally conservative variable)
 157         ri1 = sqrt(_Ui[0]); ri2 = sqrt(_Ui[_Ndim+1]);
 158         rj1 = sqrt(_Uj[0]); rj2 = sqrt(_Uj[_Ndim+1]);
 159         // Roe average formula of the velocities
 160         for(int k=0;k<_Ndim;k++)
 161         {
 162                 xi = _Ui[k+1];
 163                 xj = _Uj[k+1];
 164                 // avoid dividing by zero, if mass is zero, do not consider the distribution of such a phase
 165                 if(ri1>_precision && rj1>_precision)
 166                         _Uroe[2+k] = (xi/ri1 + xj/rj1)/(ri1 + rj1);
 167                 else if(ri1<_precision && rj1>_precision)
 168                         _Uroe[2+k] =  xj/_Uj[0];
 169                 else if(ri1>_precision && rj1<_precision)
 170                         _Uroe[2+k] =  xi/_Ui[0];
 171                 else
 172                         _Uroe[2+k] =(_Ui[k+1+_Ndim+1]/ri2 + _Uj[k+1+_Ndim+1]/rj2)/(ri2 + rj2);
 173
 174                 xi = _Ui[k+1+_Ndim+1];
 175                 xj = _Uj[k+1+_Ndim+1];
 176                 if(ri2>_precision && rj2>_precision)
 177                         _Uroe[2+k+_Ndim] = (xi/ri2 + xj/rj2)/(ri2 + rj2);
 178                 else if(ri2<_precision && rj2>_precision)
 179                         _Uroe[2+k+_Ndim] = xj/_Uj[_Ndim+1];
 180                 else if(ri2>_precision && rj2<_precision)
 181                         _Uroe[2+k+_Ndim] = xi/_Ui[_Ndim+1];
 182                 else
 183                         _Uroe[2+k+_Ndim] = (xi/ri1 + xj/rj1)/(ri1 + rj1);
 184         }
 185         if(_verbose && _nbTimeStep%_freqSave ==0)
 186         {
 187                 cout<<"Etat de Roe calcule: "<<endl;
 188                 for(int k=0;k<_nVar; k++)//At this point _Uroe[_nVar] is not yet set
 189                         cout<< _Uroe[k]<<endl;
 190         }
 191 }
 192
 193 void IsothermalTwoFluid::diffusionStateAndMatrices(const long &i,const long &j, const bool &IsBord){
 194         //sortie: matrices et etat de diffusion (m_v, q_v, m_l, q_l)
 195         _idm[0] = _nVar*i;
 196         for(int k=1; k<_nVar; k++)
 197                 _idm[k] = _idm[k-1] + 1;
 198
 199         VecGetValues(_conservativeVars, _nVar, _idm, _Ui);
 200         _idm[0] = _nVar*j;
 201         for(int k=1; k<_nVar; k++)
 202                 _idm[k] = _idm[k-1] + 1;
 203
 204         if(IsBord)
 205                 VecGetValues(_Uextdiff, _nVar, _idm, _Uj);
 206         else
 207                 VecGetValues(_conservativeVars, _nVar, _idm, _Uj);
 208
 209         for(int k=0; k<_nVar; k++)
 210                 _Udiff[k] = (_Ui[k]+_Uj[k])/2;
 211         double q_2=0;
 212         for (int i = 0; i<_Ndim;i++)
 213                 q_2+=_Udiff[i+1]*_Udiff[i+1];
 214
 215         if(_timeScheme==Implicit)
 216         {
 217                 for(int i=0; i<_nVar*_nVar;i++)
 218                         _Diffusion[i] = 0;
 219                 double mu1 = _fluides[0]->getViscosity(_Temperature);
 220                 double mu2 = _fluides[1]->getViscosity(_Temperature);
 221                 for(int idim=1;idim<_Ndim+1;idim++)
 222                 {
 223                         _Diffusion[idim*_nVar] =  mu1*_Udiff[idim]/(_Udiff[0]*_Udiff[0]);
 224                         _Diffusion[idim*_nVar+idim] = -mu1/_Udiff[0];
 225                         _Diffusion[(idim+_Ndim+1)*_nVar] =  mu2*_Udiff[idim+_Ndim+1]/(_Udiff[_Ndim+1]*_Udiff[_Ndim+1]);
 226                         _Diffusion[(idim+_Ndim+1)*_nVar+idim+_Ndim+1] = -mu2/_Udiff[_Ndim+1];
 227                 }
 228         }
 229 }
 230
 231 void IsothermalTwoFluid::convectionMatrices()
 232 {
 233         //entree: URoe = alpha, p, u1, u2 + ajout dpi pour calcul flux ultérieur
 234         //sortie: matrices Roe+  et Roe- +Roe si scheme centre
 235
 236         if(_timeScheme==Implicit && _usePrimitiveVarsInNewton)
 237                 throw CdmathException("Implicitation with primitive variables not yet available for IsothermalTwoFluid model");
 238
 239         /*Definitions */
 240         complex< double > tmp;
 241         double u1_n, u1_2, u2_n, u2_2, u_r2;
 242         u1_2 = 0; u2_2=0;
 243         u1_n = 0; u2_n=0;
 244         // relative velocity
 245         u_r2=0;
 246         for(int i=0;i<_Ndim;i++)
 247         {
 248                 u1_2 += _Uroe[2+i]*_Uroe[2+i];
 249                 u1_n += _Uroe[2+i]*_vec_normal[i];
 250                 u2_2 += _Uroe[2+i+_Ndim]*_Uroe[2+i+_Ndim];
 251                 u2_n += _Uroe[2+i+_Ndim]*_vec_normal[i];
 252                 u_r2 += (_Uroe[2+i]-_Uroe[2+i+_Ndim])*(_Uroe[2+i]-_Uroe[2+i+_Ndim]);
 253         }
 254         //Ancienne construction Mat Roe (Dm1,Dm2,Dalp,Dp)
 255         double alpha = _Uroe[0];
 256         double p = _Uroe[1];
 257         double rho1 = _fluides[0]->getDensity(p, _Temperature);
 258         double rho2 = _fluides[1]->getDensity(p, _Temperature);
 259         double dpi1 = intPressDef(alpha, u_r2, rho1, rho2);
 260         double dpi2 = dpi1;
 261         double invcsq1 = 1/_fluides[0]->vitesseSonTemperature(_Temperature,rho1);
 262         invcsq1*=invcsq1;
 263         double invcsq2 = 1/_fluides[1]->vitesseSonTemperature(_Temperature,rho2);
 264         invcsq2*=invcsq2;
 265         double g2 = 1/(alpha*rho2*invcsq1+(1-alpha)*rho1*invcsq2);
 266         double g2press=g2, g2alpha=g2;
 267         //saving dpi value for flux calculation later
 268         _Uroe[_nVar]=dpi1 ;
 269
 270         /***********Calcul des valeurs propres ********/
 271         Polynoms Poly;
 272         vector< double > pol_car= Poly.polynome_caracteristique(alpha,  1-alpha, u1_n, u2_n, rho1, rho2,invcsq1,invcsq2, dpi1, dpi2, g2press, g2alpha, g2,_precision);
 273         for(int ct=0;ct<4;ct++){
 274                 if (abs(pol_car[ct])<_precision*_precision)
 275                         pol_car[ct]=0;
 276         }
 277         if(_verbose && _nbTimeStep%_freqSave ==0)
 278         {
 279                 cout<<"pol caract= "<<endl;
 280                 for(int i =0; i<5; i++)
 281                         cout<<pol_car[i]<<"  ";
 282                 cout<< endl;
 283                 cout<<"alpha= "<<alpha<<", p= " << p << ", rho1= " << rho1<< ", rho2= " << rho2<< ", c1= " <<sqrt(1/invcsq1)<<
 284                                 ", c2= " <<sqrt(1/invcsq2)<<endl;
 285                 cout<< "u1_n= "<<u1_n<<", u2_n= "<<u2_n<< ", dpi1= "<<dpi1<< ", dpi2= "<<dpi2<< endl;
 286         }
 287         vector< complex<double> > valeurs_propres = getRacines(pol_car);
 288
 289         //On ajoute les valeurs propres triviales
 290         if(_Ndim>1)
 291         {
 292                 if( !Poly.belongTo(u1_n,valeurs_propres, _precision) )
 293                         valeurs_propres.push_back(u1_n);//vp vapor energy
 294                 if( !Poly.belongTo(u2_n,valeurs_propres, _precision) )
 295                         valeurs_propres.push_back(u2_n);//vp liquid energy
 296         }
 297         bool doubleeigenval = norm(valeurs_propres[0] - valeurs_propres[1])<_precision;//norm= suqare of the magnitude
 298         if(doubleeigenval)
 299         {
 300                 valeurs_propres[0] = valeurs_propres[valeurs_propres.size()-1];
 301                 valeurs_propres.pop_back();
 302         }
 303
 304         int taille_vp = Poly.new_tri_selectif(valeurs_propres,valeurs_propres.size(),_precision);//valeurs_propres.size();//
 305
 306         _maxvploc=0;
 307         for(int i =0; i<taille_vp; i++)
 308                 if(fabs(valeurs_propres[i].real())>_maxvploc)
 309                         _maxvploc=fabs(valeurs_propres[i].real());
 310         if(_maxvploc>_maxvp)
 311                 _maxvp=_maxvploc;
 312
 313         int existVpCplx = 0,pos_conj;
 314         double vp_imag_iter;
 315         for (int ct=0; ct<taille_vp; ct++) {
 316                 vp_imag_iter = valeurs_propres[ct].imag();
 317                 if ( fabs(vp_imag_iter) > _precision ) {
 318                         existVpCplx +=1;
 319                         if ( _part_imag_max < fabs(vp_imag_iter))
 320                                 _part_imag_max = fabs(vp_imag_iter);
 321                         //On cherhe le conjugue
 322                         pos_conj = ct+1;
 323                         while(pos_conj<taille_vp && fabs(valeurs_propres[pos_conj].imag()+vp_imag_iter)>_precision)
 324                                 pos_conj++;
 325                         if(pos_conj!=ct+1 && pos_conj<taille_vp )
 326                         {
 327                                 tmp=valeurs_propres[ct+1];
 328                                 valeurs_propres[ct+1]=valeurs_propres[pos_conj];
 329                                 valeurs_propres[pos_conj] = tmp;
 330                                 ct++;
 331                         }
 332                 }
 333         }
 334         if (existVpCplx >0)
 335                 _nbVpCplx +=1;
 336
 337         //on ordonne les deux premieres valeurs
 338         /*
 339         if(valeurs_propres[1].real()<valeurs_propres[0].real())
 340         {
 341                 tmp=valeurs_propres[0];
 342                 valeurs_propres[0]=valeurs_propres[1];
 343                 valeurs_propres[1]=tmp;
 344         }
 345          */
 346         if(_verbose && _nbTimeStep%_freqSave ==0)
 347         {
 348                 cout<<" Vp apres tri " << valeurs_propres.size()<<endl;
 349                 for(int ct =0; ct<taille_vp; ct++)
 350                         cout<< "("<<valeurs_propres[ct].real()<< ", " <<valeurs_propres[ct].imag() <<")  ";
 351                 cout<< endl;
 352         }
 353
 354         /******** Construction de la matrice de Roe *********/
 355         //lignes de masse
 356         for(int i=0; i<_nVar*_nVar;i++)
 357                 _Aroe[i]=0;
 358
 359         for(int idim=0; idim<_Ndim;idim++)
 360         {
 361                 _Aroe[1+idim]=_vec_normal[idim];
 362                 _Aroe[1+idim+_Ndim+1]=0;
 363                 _Aroe[(_Ndim+1)*_nVar+1+idim]=0;
 364                 _Aroe[(_Ndim+1)*_nVar+1+idim+_Ndim+1]=_vec_normal[idim];
 365         }
 366         //lignes de qdm
 367         for(int idim=0; idim<_Ndim;idim++)
 368         {
 369                 //premiere colonne (masse gaz)
 370                 _Aroe[                 (1+idim)*_nVar]=   (alpha *rho2*g2press+dpi1*(1-alpha)*invcsq2*g2alpha)*_vec_normal[idim] - u1_n*_Uroe[2+idim];
 371                 _Aroe[(_Ndim+1)*_nVar+ (1+idim)*_nVar]=((1-alpha)*rho2*g2press-dpi2*(1-alpha)*invcsq2*g2alpha)*_vec_normal[idim];
 372                 //colonnes intermediaires
 373                 for(int jdim=0; jdim<_Ndim;jdim++)
 374                 {
 375                         _Aroe[                 (1+idim)*_nVar + jdim + 1]         = _Uroe[      2+idim]*_vec_normal[jdim];
 376                         _Aroe[(_Ndim+1)*_nVar+ (1+idim)*_nVar + jdim + 1+_Ndim+1] = _Uroe[_Ndim+2+idim]*_vec_normal[jdim];
 377                 }
 378                 //matrice identite
 379                 _Aroe[                 (1+idim)*_nVar +          idim + 1] += u1_n;
 380                 _Aroe[(_Ndim+1)*_nVar+ (1+idim)*_nVar + _Ndim+1+ idim + 1] += u2_n;
 381                 //troisieme colonne (masse liquide)
 382                 _Aroe[                (1+idim)*_nVar + _Ndim+1]=   (alpha *rho1*g2press-dpi1*alpha*invcsq1*g2alpha)*_vec_normal[idim];
 383                 _Aroe[(_Ndim+1)*_nVar+(1+idim)*_nVar + _Ndim+1]=((1-alpha)*rho1*g2press+dpi2*alpha*invcsq1*g2alpha)*_vec_normal[idim] - u2_n*_Uroe[1+idim+_Ndim+1];
 384         }
 385
 386         /******* Construction des matrices de decentrement *****/
 387         if(_spaceScheme == centered){
 388                 if(_entropicCorrection)
 389                         throw CdmathException("IsothermalTwoFluid::convectionMatrices: entropic scheme not available for centered scheme");
 390                 for(int i=0; i<_nVar*_nVar;i++)
 391                         _absAroe[i]=0;
 392         }
 393         if( _spaceScheme ==staggered){
 394                 if(_entropicCorrection)//To do: study entropic correction for staggered
 395                         throw CdmathException("IsothermalTwoFluid::convectionMatrices: entropic scheme not yet available for staggered scheme");
 396                 /******** Construction du decentrement du type decale *********/
 397                 //lignes de masse
 398                 for(int i=0; i<_nVar*_nVar;i++)
 399                         _absAroe[i]=0;
 400
 401                 for(int idim=0; idim<_Ndim;idim++)
 402                 {
 403                         _absAroe[1+idim]=_vec_normal[idim];
 404                         _absAroe[1+idim+_Ndim+1]=0;
 405                         _absAroe[(_Ndim+1)*_nVar+1+idim]=0;
 406                         _absAroe[(_Ndim+1)*_nVar+1+idim+_Ndim+1]=_vec_normal[idim];
 407                 }
 408                 //lignes de qdm
 409                 for(int idim=0; idim<_Ndim;idim++)
 410                 {
 411                         //premiere colonne (masse gaz)
 412                         _absAroe[                 (1+idim)*_nVar]=   (-alpha *rho2*g2press+dpi1*(1-alpha)*invcsq2*g2alpha)*_vec_normal[idim] - u1_n*_Uroe[2+idim];
 413                         _absAroe[(_Ndim+1)*_nVar+ (1+idim)*_nVar]=(-(1-alpha)*rho2*g2press-dpi2*(1-alpha)*invcsq2*g2alpha)*_vec_normal[idim];
 414                         //colonnes intermediaires
 415                         for(int jdim=0; jdim<_Ndim;jdim++)
 416                         {
 417                                 _absAroe[                 (1+idim)*_nVar + jdim + 1]         = _Uroe[      2+idim]*_vec_normal[jdim];
 418                                 _absAroe[(_Ndim+1)*_nVar+ (1+idim)*_nVar + jdim + 1+_Ndim+1] = _Uroe[_Ndim+2+idim]*_vec_normal[jdim];
 419                         }
 420                         //matrice identite
 421                         _absAroe[                 (1+idim)*_nVar +          idim + 1] += u1_n;
 422                         _absAroe[(_Ndim+1)*_nVar+ (1+idim)*_nVar + _Ndim+1+ idim + 1] += u2_n;
 423                         //troisieme colonne (masse liquide)
 424                         _absAroe[                (1+idim)*_nVar + _Ndim+1]=   (-alpha *rho1*g2press-dpi1*alpha*invcsq1*g2alpha)*_vec_normal[idim];
 425                         _absAroe[(_Ndim+1)*_nVar+(1+idim)*_nVar + _Ndim+1]=(-(1-alpha)*rho1*g2press+dpi2*alpha*invcsq1*g2alpha)*_vec_normal[idim] - u2_n*_Uroe[1+idim+_Ndim+1];
 426                 }
 427
 428                 double signu1,signu2;
 429                 if(u1_n>0)
 430                         signu1=1;
 431                 else if (u1_n<0)
 432                         signu1=-1;
 433                 else
 434                         signu1=0;
 435                 if(u2_n>0)
 436                         signu2=1;
 437                 else if (u2_n<0)
 438                         signu2=-1;
 439                 else
 440                         signu2=0;
 441
 442                 for(int i=0; i<(1+_Ndim)*_nVar;i++){
 443                         _absAroe[i] *= signu1;
 444                         _absAroe[i+(1+_Ndim)*_nVar] *= signu2;
 445                 }
 446         }
 447         if(_spaceScheme==upwind || _spaceScheme ==lowMach)
 448         {
 449                 vector< complex< double > > y (taille_vp,0);
 450                 Polynoms Poly;
 451                 for( int i=0 ; i<taille_vp ; i++)
 452                         y[i] = Poly.abs_generalise(valeurs_propres[i]);
 453
 454                 if(_entropicCorrection)
 455                 {
 456                         entropicShift(_vec_normal);
 457                         y[0] +=_entropicShift[0];
 458                         y[taille_vp-1] +=_entropicShift[2];
 459                         for( int i=1 ; i<taille_vp-1 ; i++)
 460                                 y[i] +=_entropicShift[1];
 461                 }
 462
 463                 Poly.abs_par_interp_directe(taille_vp,valeurs_propres, _Aroe, _nVar,_precision, _absAroe,y);
 464                 if( _spaceScheme ==pressureCorrection){
 465                         for( int i=0 ; i<_Ndim ; i++)
 466                                 for( int j=0 ; j<_Ndim ; j++){
 467                                         _absAroe[(1+i)*_nVar+1+j]-=alpha*(valeurs_propres[1].real()-valeurs_propres[0].real())/2*_vec_normal[i]*_vec_normal[j];
 468                                         _absAroe[(2+_Ndim+i)*_nVar+2+_Ndim+j]-=(1-alpha)*(valeurs_propres[1].real()-valeurs_propres[0].real())/2*_vec_normal[i]*_vec_normal[j];
 469                                 }
 470                 }
 471                 else if( _spaceScheme ==lowMach){
 472                         double M=max(fabs(u1_2),fabs(u2_2))/_maxvploc;
 473                         for( int i=0 ; i<_Ndim ; i++)
 474                                 for( int j=0 ; j<_Ndim ; j++){
 475                                         _absAroe[(1+i)*_nVar+1+j]-=(1-M)*alpha*(valeurs_propres[1].real()-valeurs_propres[0].real())/2*_vec_normal[i]*_vec_normal[j];
 476                                         _absAroe[(2+_Ndim+i)*_nVar+2+_Ndim+j]-=(1-M)*(1-alpha)*(valeurs_propres[1].real()-valeurs_propres[0].real())/2*_vec_normal[i]*_vec_normal[j];
 477                                 }
 478                 }
 479
 480         }
 481         //Calcul de la matrice signe pour VFFC, VFRoe et décentrement des termes source
 482         vector< complex< double > > valeurs_propres_dist(taille_vp,0);
 483         for( int i=0 ; i<taille_vp ; i++)
 484                 valeurs_propres_dist[i] = valeurs_propres[i];
 485
 486         if(_entropicCorrection || _spaceScheme ==pressureCorrection || _spaceScheme ==lowMach){
 487                 InvMatriceRoe( valeurs_propres_dist);
 488                 Poly.matrixProduct(_absAroe, _nVar, _nVar, _invAroe, _nVar, _nVar, _signAroe);
 489         }
 490         else if (_spaceScheme==upwind)//upwind sans entropic
 491                 SigneMatriceRoe( valeurs_propres_dist);
 492         else if (_spaceScheme==centered)//centre  sans entropic
 493         {
 494                 for(int i=0; i<_nVar*_nVar;i++)
 495                         _signAroe[i] = 0;
 496         }
 497         else  if(_spaceScheme ==staggered )
 498         {
 499                 double signu1,signu2;
 500                 if(u1_n>0)
 501                         signu1=1;
 502                 else if (u1_n<0)
 503                         signu1=-1;
 504                 else
 505                         signu1=0;
 506                 if(u2_n>0)
 507                         signu2=1;
 508                 else if (u2_n<0)
 509                         signu2=-1;
 510                 else
 511                         signu2=0;
 512                 for(int i=0; i<_nVar*_nVar;i++)
 513                         _signAroe[i] = 0;
 514                 _signAroe[0] = signu1;
 515                 _signAroe[(1+_Ndim)*_nVar +1+_Ndim] = signu2;
 516                 for(int i=2; i<_nVar-1;i++){
 517                         _signAroe[i*_nVar+i] = -signu1;
 518                         _signAroe[(i+1+_Ndim)*_nVar+i+1+_Ndim] = -signu2;
 519                 }
 520         }
 521         else
 522                 throw CdmathException("IsothermalTwoFluid::convectionMatrices: well balanced option not treated");
 523
 524         for(int i=0; i<_nVar*_nVar;i++)
 525         {
 526                 _AroeMinus[i] = (_Aroe[i]-_absAroe[i])/2;
 527                 _AroePlus[i]  = (_Aroe[i]+_absAroe[i])/2;
 528         }
 529         if(_timeScheme==Implicit && _usePrimitiveVarsInNewton)//Implicitation using primitive variables
 530                 for(int i=0; i<_nVar*_nVar;i++)
 531                         _AroeMinusImplicit[i] = (_AroeImplicit[i]-_absAroeImplicit[i])/2;
 532         else
 533                 for(int i=0; i<_nVar*_nVar;i++)
 534                         _AroeMinusImplicit[i] = _AroeMinus[i];
 535
 536         if(_verbose && _nbTimeStep%_freqSave ==0)
 537         {
 538                 cout<<endl<<"Matrice de Roe"<<endl;
 539                 for(int i=0; i<_nVar;i++)
 540                 {
 541                         for(int j=0; j<_nVar;j++)
 542                                 cout << _Aroe[i*_nVar+j]<< " , ";
 543                         cout<<endl;
 544                 }
 545                 cout<<"Valeur absolue matrice de Roe"<<endl;
 546                 for(int i=0; i<_nVar;i++){
 547                         for(int j=0; j<_nVar;j++)
 548                                 cout<<_absAroe[i*_nVar+j]<<" , ";
 549                         cout<<endl;
 550                 }
 551                 cout<<endl<<"Matrice _AroeMinus"<<endl;
 552                 for(int i=0; i<_nVar;i++)
 553                 {
 554                         for(int j=0; j<_nVar;j++)
 555                                 cout << _AroeMinus[i*_nVar+j]<< " , ";
 556                         cout<<endl;
 557                 }
 558                 cout<<endl<<"Matrice _AroePlus"<<endl;
 559                 for(int i=0; i<_nVar;i++)
 560                 {
 561                         for(int j=0; j<_nVar;j++)
 562                                 cout << _AroePlus[i*_nVar+j]<< " , ";
 563                         cout<<endl;
 564                 }
 565         }
 566 }
 567
 568 void IsothermalTwoFluid::setBoundaryState(string nameOfGroup, const int &j,double *normale){
 569         //To do controle signe des vitesses pour CL entree/sortie
 570         int k;
 571         _idm[0] = _nVar*j;
 572         for(k=1; k<_nVar; k++)
 573                 _idm[k] = _idm[k-1] + 1;
 574
 575         VecGetValues(_conservativeVars, _nVar, _idm, _externalStates);//On initialise l'état fantôme avec l'état interne
 576         double q1_n=0, q2_n=0;//quantité de mouvement normale à la face limite
 577         for(k=0; k<_Ndim; k++){
 578                 q1_n+=_externalStates[(k+1)]*normale[k];
 579                 q2_n+=_externalStates[(k+1+1+_Ndim)]*normale[k];
 580         }
 581
 582         if(_verbose && _nbTimeStep%_freqSave ==0)
 583         {
 584                 cout << "Boundary conditions for group "<< nameOfGroup<< ", inner cell j= "<<j << " face unit normal vector "<<endl;
 585                 for(k=0; k<_Ndim; k++){
 586                         cout<<normale[k]<<", ";
 587                 }
 588                 cout<<endl;
 589         }
 590         if (_limitField[nameOfGroup].bcType==Wall){
 591
 592                 //Pour la convection, inversion du sens des vitesses
 593                 for(k=0; k<_Ndim; k++){
 594                         _externalStates[(k+1)]-= 2*q1_n*normale[k];
 595                         _externalStates[(k+1+1+_Ndim)]-= 2*q2_n*normale[k];
 596                 }
 597
 598                 _idm[0] = 0;
 599                 for(k=1; k<_nVar; k++)
 600                         _idm[k] = _idm[k-1] + 1;
 601
 602                 VecAssemblyBegin(_Uext);
 603                 VecSetValues(_Uext, _nVar, _idm, _externalStates, INSERT_VALUES);
 604                 VecAssemblyEnd(_Uext);
 605
 606                 //Pour la diffusion, paroi à vitesses imposees
 607                 _externalStates[1]=_externalStates[0]*_limitField[nameOfGroup].v_x[0];
 608                 _externalStates[2+_Ndim]=_externalStates[1+_Ndim]*_limitField[nameOfGroup].v_x[1];
 609                 if(_Ndim>1)
 610                 {
 611                         _externalStates[2]=_externalStates[0]*_limitField[nameOfGroup].v_y[0];
 612                         _externalStates[3+_Ndim]=_externalStates[1+_Ndim]*_limitField[nameOfGroup].v_y[1];
 613                         if(_Ndim==3)
 614                         {
 615                                 _externalStates[3]=_externalStates[0]*_limitField[nameOfGroup].v_z[0];
 616                                 _externalStates[4+_Ndim]=_externalStates[1+_Ndim]*_limitField[nameOfGroup].v_z[1];
 617                         }
 618                 }
 619                 VecAssemblyBegin(_Uextdiff);
 620                 VecSetValues(_Uextdiff, _nVar, _idm, _externalStates, INSERT_VALUES);
 621                 VecAssemblyEnd(_Uextdiff);
 622         }
 623         else if (_limitField[nameOfGroup].bcType==Neumann){
 624                 _idm[0] = 0;
 625                 for(k=1; k<_nVar; k++)
 626                         _idm[k] = _idm[k-1] + 1;
 627
 628                 VecAssemblyBegin(_Uext);
 629                 VecSetValues(_Uext, _nVar, _idm, _externalStates, INSERT_VALUES);
 630                 VecAssemblyEnd(_Uext);
 631
 632                 VecAssemblyBegin(_Uextdiff);
 633                 VecSetValues(_Uextdiff, _nVar, _idm, _externalStates, INSERT_VALUES);
 634                 VecAssemblyEnd(_Uextdiff);
 635         }
 636         else if (_limitField[nameOfGroup].bcType==Inlet){
 637                 _idm[0] = _nVar*j;
 638                 for(k=1; k<_nVar; k++)
 639                         _idm[k] = _idm[k-1] + 1;
 640
 641                 VecGetValues(_primitiveVars, _nVar, _idm, _Vj);
 642                 double alpha=_limitField[nameOfGroup].alpha;
 643                 double pression=_Vj[1];
 644                 double T=_Temperature;
 645                 double rho_v=_fluides[0]->getDensity(pression,T);
 646                 double rho_l=_fluides[1]->getDensity(pression,T);
 647                 _externalStates[0]=alpha*rho_v;
 648                 _externalStates[1]=alpha*rho_v*(_limitField[nameOfGroup].v_x[0]);
 649                 _externalStates[1+_Ndim]=(1-alpha)*rho_l;
 650                 _externalStates[2+_Ndim]=(1-alpha)*rho_l*(_limitField[nameOfGroup].v_x[1]);
 651                 if(_Ndim>1)
 652                 {
 653                         _externalStates[2]=_externalStates[0]*_limitField[nameOfGroup].v_y[0];
 654                         _externalStates[3+_Ndim]=_externalStates[1+_Ndim]*_limitField[nameOfGroup].v_y[1];
 655                         if(_Ndim==3)
 656                         {
 657                                 _externalStates[3]=_externalStates[0]*_limitField[nameOfGroup].v_z[0];
 658                                 _externalStates[4+_Ndim]=_externalStates[1+_Ndim]*_limitField[nameOfGroup].v_z[1];
 659                         }
 660                 }
 661                 _idm[0] = 0;
 662                 for(k=1; k<_nVar; k++)
 663                         _idm[k] = _idm[k-1] + 1;
 664                 VecAssemblyBegin(_Uext);
 665                 VecAssemblyBegin(_Uextdiff);
 666                 VecSetValues(_Uext, _nVar, _idm, _externalStates, INSERT_VALUES);
 667                 VecSetValues(_Uextdiff, _nVar, _idm, _externalStates, INSERT_VALUES);
 668                 VecAssemblyEnd(_Uext);
 669                 VecAssemblyEnd(_Uextdiff);
 670         }
 671         else if (_limitField[nameOfGroup].bcType==InletPressure){
 672                 //Computation of the hydrostatic contribution : scalar product between gravity vector and position vector
 673                 Cell Cj=_mesh.getCell(j);
 674                 double hydroPress=Cj.x()*_GravityField3d[0];
 675                 if(_Ndim>1){
 676                         hydroPress+=Cj.y()*_GravityField3d[1];
 677                         if(_Ndim>2)
 678                                 hydroPress+=Cj.z()*_GravityField3d[2];
 679                 }
 680                 hydroPress*=_externalStates[0]+_externalStates[_Ndim];//multiplication by rho the total density
 681
 682                 //Building the external state
 683                 _idm[0] = _nVar*j;
 684                 for(k=1; k<_nVar; k++)
 685                         _idm[k] = _idm[k-1] + 1;
 686
 687                 VecGetValues(_primitiveVars, _nVar, _idm, _Vj);
 688                 double pression=_limitField[nameOfGroup].p+hydroPress;
 689                 double alpha=_limitField[nameOfGroup].alpha;
 690                 double T=_Temperature;
 691                 double rho_v=_fluides[0]->getDensity(pression,T);
 692                 double rho_l=_fluides[1]->getDensity(pression,T);
 693                 _externalStates[0]=alpha*rho_v;
 694                 _externalStates[1+_Ndim]=(1-alpha)*rho_l;
 695
 696                 for(k=1;k<1+_Ndim;k++){
 697                         _externalStates[k]=_externalStates[0]*_Vj[1+k];
 698                         _externalStates[k+1+_Ndim]=_externalStates[1+_Ndim]*_Vj[k+1+_Ndim];
 699                 }
 700                 _idm[0] = 0;
 701                 for(k=1; k<_nVar; k++)
 702                         _idm[k] = _idm[k-1] + 1;
 703                 VecAssemblyBegin(_Uext);
 704                 VecAssemblyBegin(_Uextdiff);
 705                 VecSetValues(_Uext, _nVar, _idm, _externalStates, INSERT_VALUES);
 706                 VecSetValues(_Uextdiff, _nVar, _idm, _externalStates, INSERT_VALUES);
 707                 VecAssemblyEnd(_Uext);
 708                 VecAssemblyEnd(_Uextdiff);
 709
 710                 if(_verbose && _nbTimeStep%_freqSave ==0)
 711                 {
 712                         cout<<"Etat fantôme InletPressure"<<endl;
 713                         for(int k=0;k<_nVar;k++)
 714                                 cout<<_externalStates[k]<<endl;
 715                 }
 716         }
 717         else if (_limitField[nameOfGroup].bcType==Outlet){
 718                 _idm[0] = _nVar*j;
 719                 for(k=1; k<_nVar; k++)
 720                         _idm[k] = _idm[k-1] + 1;
 721
 722                 //Computation of the hydrostatic contribution : scalar product between gravity vector and position vector
 723                 Cell Cj=_mesh.getCell(j);
 724                 double hydroPress=Cj.x()*_GravityField3d[0];
 725                 if(_Ndim>1){
 726                         hydroPress+=Cj.y()*_GravityField3d[1];
 727                         if(_Ndim>2)
 728                                 hydroPress+=Cj.z()*_GravityField3d[2];
 729                 }
 730                 hydroPress*=_externalStates[0]+_externalStates[_Ndim];//multiplication by rho the total density
 731
 732                 //Building the external state
 733                 VecGetValues(_primitiveVars, _nVar, _idm,_Vj);
 734                 double pression_int=_Vj[1];
 735                 double pression_ext=_limitField[nameOfGroup].p+hydroPress;
 736                 double T=_Vj[_nVar-1];
 737                 double rho_v_int=_fluides[0]->getDensity(pression_int,T);
 738                 double rho_l_int=_fluides[1]->getDensity(pression_int,T);
 739                 double rho_v_ext=_fluides[0]->getDensity(pression_ext,T);
 740                 double rho_l_ext=_fluides[1]->getDensity(pression_ext,T);
 741
 742                 for(k=0;k<1+_Ndim;k++){
 743                         _externalStates[k]*=rho_v_ext/rho_v_int;
 744                         _externalStates[k+1+_Ndim]*=rho_l_ext/rho_l_int;
 745                 }
 746                 _idm[0] = 0;
 747                 for(k=1; k<_nVar; k++)
 748                         _idm[k] = _idm[k-1] + 1;
 749                 VecAssemblyBegin(_Uext);
 750                 VecAssemblyBegin(_Uextdiff);
 751                 VecSetValues(_Uext, _nVar, _idm, _externalStates, INSERT_VALUES);
 752                 VecSetValues(_Uextdiff, _nVar, _idm, _externalStates, INSERT_VALUES);
 753                 VecAssemblyEnd(_Uext);
 754                 VecAssemblyEnd(_Uextdiff);
 755         }
 756         else{
 757                 cout<<"!!!!!!!!!!!!!!!!! Error IsothermalTwoFluid::setBoundaryState !!!!!!!!!!"<<endl;
 758                 cout<<"!!!!!!!!!!!!! Boundary condition not set for boundary named"<<nameOfGroup<< ", _limitField[nameOfGroup].bcType= "<<_limitField[nameOfGroup].bcType<<endl;
 759                 cout<<"Accepted boundary condition are Neumann, Wall, Inlet, and Outlet"<<endl;
 760                 throw CdmathException("Unknown boundary condition");
 761         }
 762 }
 763
 764 void IsothermalTwoFluid::addDiffusionToSecondMember
 765 (               const int &i,
 766                 const int &j,
 767                 bool isBord)
 768
 769 {
 770         double mu1 = _fluides[0]->getViscosity(_Temperature);
 771         double mu2 = _fluides[1]->getViscosity(_Temperature);
 772
 773         if(mu1==0 && mu2==0)
 774                 return;
 775
 776         //extraction des valeurs
 777         _idm[0] = _nVar*i;
 778         for(int k=1; k<_nVar; k++)
 779                 _idm[k] = _idm[k-1] + 1;
 780
 781         VecGetValues(_primitiveVars, _nVar, _idm, _Vi);
 782         if (_verbose && _nbTimeStep%_freqSave ==0)
 783         {
 784                 cout << "Contribution diffusion: variables primitives maille " << i<<endl;
 785                 for(int q=0; q<_nVar; q++)
 786                 {
 787                         cout << _Vi[q] << endl;
 788                 }
 789                 cout << endl;
 790         }
 791
 792         if(!isBord ){
 793                 for(int k=0; k<_nVar; k++)
 794                         _idm[k] = _nVar*j + k;
 795                 VecGetValues(_primitiveVars, _nVar, _idm, _Vj);
 796         }
 797         else
 798         {
 799                 for(int k=0; k<_nVar; k++)
 800                         _idm[k] = k;
 801
 802                 VecGetValues(_Uextdiff, _nVar, _idm, _phi);
 803                 consToPrim(_phi,_Vj);
 804         }
 805
 806         if (_verbose && _nbTimeStep%_freqSave ==0)
 807         {
 808                 cout << "Contribution diffusion: variables primitives maille " <<j <<endl;
 809                 for(int q=0; q<_nVar; q++)
 810                 {
 811                         cout << _Vj[q] << endl;
 812                 }
 813                 cout << endl;
 814         }
 815
 816
 817         double alpha=(_Vj[0]+_Vi[0])/2;
 818         //on n'a pas de contribution sur la masse
 819         _phi[0]=0;
 820         _phi[_Ndim+1]=0;
 821         //contribution visqueuse sur la quantite de mouvement
 822         for(int k=1; k<_Ndim+1; k++)
 823         {
 824                 _phi[k]         = _inv_dxi*2/(1/_inv_dxi+1/_inv_dxj)*alpha*mu1*(_Vj[k] - _Vi[k]);//attention car primitif=alpha p u1 u2
 825                 _phi[k+_Ndim+1] = _inv_dxi*2/(1/_inv_dxi+1/_inv_dxj)*(1-alpha)*mu2*(_Vj[1+k+_Ndim] - _Vi[1+k+_Ndim]);
 826         }
 827
 828         _idm[0] = i;
 829         VecSetValuesBlocked(_b, 1, _idm, _phi, ADD_VALUES);
 830
 831         if(_verbose && _nbTimeStep%_freqSave ==0)
 832         {
 833                 cout << "Contribution diffusion au 2nd membre pour la maille " << i << ": "<<endl;
 834                 for(int q=0; q<_nVar; q++)
 835                 {
 836                         cout << _phi[q] << endl;
 837                 }
 838                 cout << endl;
 839         }
 840
 841         if(!isBord)
 842         {
 843                 //On change de signe pour l'autre contribution
 844                 for(int k=0; k<_nVar; k++)
 845                         _phi[k] *= -_inv_dxj/_inv_dxi;
 846                 _idm[0] = j;
 847
 848                 VecSetValuesBlocked(_b, 1, _idm, _phi, ADD_VALUES);
 849         }
 850
 851         if(_verbose && _nbTimeStep%_freqSave ==0)
 852         {
 853                 cout << "Contribution diffusion au 2nd membre pour la maille  " << j << ": "<<endl;
 854                 for(int q=0; q<_nVar; q++)
 855                 {
 856                         cout << _phi[q] << endl;
 857                 }
 858                 cout << endl;
 859
 860                 if(_timeScheme==Implicit)
 861                 {
 862                         cout << "Matrice de diffusion D, pour le couple (" << i << "," << j<< "):" << endl;
 863                         for(int i=0; i<_nVar; i++)
 864                         {
 865                                 for(int j=0; j<_nVar; j++)
 866                                         cout << _Diffusion[i*_nVar+j]<<", ";
 867                                 cout << endl;
 868                         }
 869                         cout << endl;
 870                 }
 871         }
 872 }
 873
 874 void IsothermalTwoFluid::sourceVector(PetscScalar * Si,PetscScalar * Ui,PetscScalar * Vi, int i)
 875 {
 876         double m1=Ui[0],m2=Ui[1+_Ndim],alpha=Vi[0], P=Vi[1];
 877         double norm_ur=0, Gamma;
 878         for(int k=0; k<_Ndim; k++)
 879                 norm_ur+=(Vi[2+k]-Vi[2+k+_Ndim])*(Vi[2+k]-Vi[2+k+_Ndim]);
 880         norm_ur=sqrt(norm_ur);
 881
 882         if(i>=0 &&_Temperature>_Tsat && alpha<1-_precision)
 883                 Gamma=_heatPowerField(i)/_latentHeat;
 884         else
 885                 Gamma=0;
 886         for(int k=1; k<_Ndim+1; k++)
 887         {
 888                 //cout<<"Vi[1+"<<k+_Ndim<<"]="<<Vi[1+k+_Ndim]<<endl;
 889                 Si[k] =_gravite[k]*m1 -_dragCoeffs[0]*norm_ur*(Vi[1+k]-Vi[1+k+_Ndim])+ Gamma*Vi[1+k+_Ndim];//interfacial velocity= ul
 890                 Si[k+_Ndim+1] =_gravite[k+_Ndim+1]*m2 + _dragCoeffs[0]*norm_ur*(Vi[1+k]-Vi[1+k+_Ndim])- Gamma*Vi[1+k+_Ndim];
 891         }
 892         if(true){//heated boiling
 893                 Si[0]=Gamma;
 894                 Si[1+_Ndim]=-Gamma;
 895         }
 896         else if (P<_Psat && alpha<1-_precision){//flash boiling
 897                 Si[0]=-_dHsatl_over_dp*_dp_over_dt(i)/_latentHeat;
 898                 Si[1+_Ndim]=_dHsatl_over_dp*_dp_over_dt(i)/_latentHeat;
 899         }
 900         else{
 901                 Si[0]=0;
 902                 Si[1+_Ndim]=0;
 903         }
 904
 905         if(_timeScheme==Implicit)
 906         {
 907                 for(int i=0; i<_nVar*_nVar;i++)
 908                         _GravityImplicitationMatrix[i] = 0;
 909                 for(int i=0; i<_nVar/2;i++)
 910                         _GravityImplicitationMatrix[i*_nVar]=-_gravite[i];
 911                 for(int i=_nVar/2; i<_nVar;i++)
 912                         _GravityImplicitationMatrix[i*_nVar+_nVar/2]=-_gravite[i];
 913         }
 914
 915         if(_verbose && _nbTimeStep%_freqSave ==0)
 916         {
 917                 cout<<"IsothermalTwoFluid::sourceVector"<<endl;
 918                 cout<<"Ui="<<endl;
 919                 for(int k=0;k<_nVar;k++)
 920                         cout<<Ui[k]<<", ";
 921                 cout<<endl;
 922                 cout<<"Vi="<<endl;
 923                 for(int k=0;k<_nVar;k++)
 924                         cout<<Vi[k]<<", ";
 925                 cout<<endl;
 926                 cout<<"Si="<<endl;
 927                 for(int k=0;k<_nVar;k++)
 928                         cout<<Si[k]<<", ";
 929                 cout<<endl;
 930                 if(_timeScheme==Implicit)
 931                         displayMatrix(_GravityImplicitationMatrix, _nVar, "Gravity implicitation matrix");
 932         }
 933 }
 934 void IsothermalTwoFluid::pressureLossVector(PetscScalar * pressureLoss, double K, PetscScalar * Ui, PetscScalar * Vi, PetscScalar * Uj, PetscScalar * Vj)
 935 {
 936         double norm_u1=0, u1_n=0, norm_u2=0, u2_n=0, m1, m2;
 937         for(int i=0;i<_Ndim;i++){
 938                 u1_n += _Uroe[2+i]      *_vec_normal[i];
 939                 u2_n += _Uroe[2+i+_Ndim]*_vec_normal[i];
 940         }
 941         pressureLoss[0]=0;
 942         pressureLoss[1+_Ndim]=0;
 943         if(u1_n>0){
 944                 for(int i=0;i<_Ndim;i++)
 945                         norm_u1 += Vi[1+i]*Vi[1+i];
 946                 norm_u1=sqrt(norm_u1);
 947                 m1=Ui[0];
 948                 for(int i=0;i<_Ndim;i++)
 949                         pressureLoss[1+i]=-K*m1*norm_u1*Vi[1+i];
 950         }
 951         else{
 952                 for(int i=0;i<_Ndim;i++)
 953                         norm_u1 += Vj[1+i]*Vj[1+i];
 954                 norm_u1=sqrt(norm_u1);
 955                 m1=Uj[0];
 956                 for(int i=0;i<_Ndim;i++)
 957                         pressureLoss[1+i]=-K*m1*norm_u1*Vj[1+i];
 958         }
 959         if(u2_n>0){
 960                 for(int i=0;i<_Ndim;i++)
 961                         norm_u2 += Vi[2+i+_Ndim]*Vi[2+i+_Ndim];
 962                 norm_u2=sqrt(norm_u2);
 963                 m2=Ui[1+_Ndim];
 964                 for(int i=0;i<_Ndim;i++)
 965                         pressureLoss[2+i+_Ndim]=-K*m2*norm_u2*Vi[2+i+_Ndim];
 966         }
 967         else{
 968                 for(int i=0;i<_Ndim;i++)
 969                         norm_u2 += Vj[2+i+_Ndim]*Vj[2+i+_Ndim];
 970                 norm_u2=sqrt(norm_u2);
 971                 m2=Uj[1+_Ndim];
 972                 for(int i=0;i<_Ndim;i++)
 973                         pressureLoss[2+i+_Ndim]=-K*m2*norm_u2*Vj[2+i+_Ndim];
 974         }
 975         if(_verbose && _nbTimeStep%_freqSave ==0)
 976         {
 977                 cout<<"IsothermalTwoFluid::pressureLossVector K= "<<K<<endl;
 978                 cout<<"Ui="<<endl;
 979                 for(int k=0;k<_nVar;k++)
 980                         cout<<Ui[k]<<", ";
 981                 cout<<endl;
 982                 cout<<"Vi="<<endl;
 983                 for(int k=0;k<_nVar;k++)
 984                         cout<<Vi[k]<<", ";
 985                 cout<<endl;
 986                 cout<<"Uj="<<endl;
 987                 for(int k=0;k<_nVar;k++)
 988                         cout<<Uj[k]<<", ";
 989                 cout<<endl;
 990                 cout<<"Vj="<<endl;
 991                 for(int k=0;k<_nVar;k++)
 992                         cout<<Vj[k]<<", ";
 993                 cout<<endl;
 994                 cout<<"pressureLoss="<<endl;
 995                 for(int k=0;k<_nVar;k++)
 996                         cout<<pressureLoss[k]<<", ";
 997                 cout<<endl;
 998         }
 999 }
1000
1001 void IsothermalTwoFluid::porosityGradientSourceVector()
1002 {
1003         double u1_ni=0, u1_nj=0, u2_ni=0, u2_nj=0, rho1i, rho2i, rho1j, rho2j, pi=_Vi[1], pj=_Vj[1], pij1, pij2, alphaij=_Uroe[0];
1004         for(int i=0;i<_Ndim;i++) {
1005                 u1_ni += _Vi[2+i]*_vec_normal[i];
1006                 u2_ni += _Vi[2+_Ndim+i]*_vec_normal[i];
1007                 u1_nj += _Vj[2+i]*_vec_normal[i];
1008                 u2_nj += _Vj[2+_Ndim+i]*_vec_normal[i];
1009         }
1010         _porosityGradientSourceVector[0]=0;
1011         _porosityGradientSourceVector[1+_Ndim]=0;
1012         rho1i = _fluides[0]->getDensity(pi, _Temperature);
1013         rho2i = _fluides[1]->getDensity(pi, _Temperature);
1014         rho1j = _fluides[0]->getDensity(pj, _Temperature);
1015         rho2j = _fluides[1]->getDensity(pj, _Temperature);
1016         pij1=(pi+pj)/2+rho1i*rho1j/2/(rho1i+rho1j)*(u1_ni-u1_nj)*(u1_ni-u1_nj);
1017         pij2=(pi+pj)/2+rho2i*rho2j/2/(rho2i+rho2j)*(u2_ni-u2_nj)*(u2_ni-u2_nj);
1018         for(int i=0;i<_Ndim;i++){
1019                 _porosityGradientSourceVector[1+i]      =alphaij*pij1*(_porosityi-_porosityj)*2/(1/_inv_dxi+1/_inv_dxj);
1020                 _porosityGradientSourceVector[2+_Ndim+i]=alphaij*pij2*(_porosityi-_porosityj)*2/(1/_inv_dxi+1/_inv_dxj);
1021         }
1022 }
1023
1024 /* Funtion of equations of states */
1025 double IsothermalTwoFluid::ecartPression(double m1,double m2, double alpha, double e1, double e2){
1026         if(alpha>_precision*_precision&& alpha<1-_precision*_precision)
1027                 return _fluides[0]->getPressure((m1/alpha)*e1,m1/alpha) - _fluides[1]->getPressure((m2/(1-alpha))*e2,m2/(1-alpha));
1028         else if(alpha<=_precision*_precision)
1029         {
1030                 //cout<<"Warning ecartPression, alpha close to 0"<<endl;
1031                 //       if(m1<_precision*_precision*_precision)
1032                 //      return 0;
1033                 //       else
1034                 return alpha/_precision*_precision;
1035         }
1036         else
1037         {
1038                 //cout<<"Warning ecartPression, alpha close to 1"<<endl;
1039                 //       if(m2<_precision*_precision*_precision)
1040                 //      return 0;
1041                 //       else
1042                 return -(1-alpha)/_precision*_precision;
1043         }
1044 }
1045
1046 double IsothermalTwoFluid::ecartPressionDerivee(double m1,double m2, double alpha, double e1, double e2){
1047         if(alpha>_precision*_precision && alpha<1-_precision*_precision )
1048                 return -(m1/alpha)/alpha*e1*_fluides[0]->getPressureDerivativeRhoE() - (m2/(1-alpha))/(1-alpha)*e2*_fluides[1]->getPressureDerivativeRhoE();
1049         else if (alpha<_precision*_precision)
1050                 return -1/_precision*_precision;
1051         else
1052                 return 1/_precision*_precision;
1053 }
1054
1055 double IsothermalTwoFluid::intPressDef(double alpha, double u_r2, double rho1, double rho2)
1056 {
1057         return  _intPressCoeff*alpha*(1-alpha)*rho1*rho2*u_r2/( alpha*rho2+(1-alpha)*rho1)
1058                         +alpha*(1-alpha)*rho1*rho2*u_r2/((alpha*rho2+(1-alpha)*rho1)*(alpha*rho2+(1-alpha)*rho1)*(alpha*rho2+(1-alpha)*rho1)*(alpha*rho2+(1-alpha)*rho1))*u_r2
1059                         *(alpha*alpha*rho2-(1-alpha)*(1-alpha)*rho1)
1060                         *(alpha*alpha*rho2*rho2/(_fluides[0]->vitesseSonTemperature(_Temperature,rho1)*_fluides[0]->vitesseSonTemperature(_Temperature,rho1))
1061                                         -(1-alpha)*(1-alpha)*rho1*rho1/(_fluides[1]->vitesseSonTemperature(_Temperature,rho2)*_fluides[1]->vitesseSonTemperature(_Temperature,rho2)));
1062 }
1063
1064 void IsothermalTwoFluid::entropicShift(double* n)
1065 {
1066         vector< double > pol_car;
1067
1068         /*Left values */
1069         double u1_n = 0, u1_2 = 0, u2_n = 0, u2_2 = 0, u_r2 = 0;
1070         for(int i=0;i<_Ndim;i++)
1071         {
1072                 u1_2 += _l[2+i]*_l[2+i];
1073                 u1_n += _l[2+i]*n[i];
1074                 u2_2 += _l[1+i+1+_Ndim]*_l[1+i+1+_Ndim];
1075                 u2_n += _l[1+i+1+_Ndim]*n[i];
1076                 u_r2 += (_l[2+i]-_l[1+i+1+_Ndim])*(_l[2+i]-_l[1+i+1+_Ndim]);
1077         }
1078         double alpha = _l[0];
1079         double p = _l[1];
1080         double rho1 = _fluides[0]->getDensity(p, _Temperature);
1081         double rho2 = _fluides[1]->getDensity(p, _Temperature);
1082         double dpi1 = intPressDef(alpha, u_r2, rho1, rho2);
1083         double dpi2 = dpi1;
1084         double invcsq1 = 1/_fluides[0]->vitesseSonTemperature(_Temperature,rho1);
1085         invcsq1*=invcsq1;
1086         double invcsq2 = 1/_fluides[1]->vitesseSonTemperature(_Temperature,rho2);
1087         invcsq2*=invcsq2;
1088
1089         Polynoms Poly;
1090         pol_car= Poly.polynome_caracteristique(alpha,  1-alpha, u1_n, u2_n, rho1, rho2, invcsq1, invcsq2, dpi1, dpi2);
1091         for(int ct=0;ct<4;ct++){
1092                 if (abs(pol_car[ct])<_precision*_precision)
1093                         pol_car[ct]=0;
1094         }
1095         vector< complex<double> > vp_left = getRacines(pol_car);
1096         int taille_vp_left = Poly.new_tri_selectif(vp_left,vp_left.size(),_precision);
1097
1098         if(_verbose && _nbTimeStep%_freqSave ==0)
1099         {
1100                 cout<<"Entropic shift left eigenvalues: "<<endl;
1101                 for(unsigned int ct =0; ct<vp_left.size(); ct++)
1102                         cout<<"("<< vp_left[ct].real()<< ", " <<vp_left[ct].imag() << ")";
1103                 cout<<endl;
1104         }
1105
1106         /*right values */
1107         u1_2 = 0; u2_2=0;
1108         u1_n = 0; u2_n=0;
1109         u_r2=0;
1110         for(int i=0;i<_Ndim;i++)
1111         {
1112                 u1_2 += _r[2+i]*_r[2+i];
1113                 u1_n += _r[2+i]*n[i];
1114                 u2_2 += _r[1+i+1+_Ndim]*_r[1+i+1+_Ndim];
1115                 u2_n += _r[1+i+1+_Ndim]*n[i];
1116                 u_r2 += (_r[2+i]-_r[1+i+1+_Ndim])*(_r[2+i]-_r[1+i+1+_Ndim]);
1117         }
1118         alpha = _r[0];
1119         p = _r[1];
1120         rho1 = _fluides[0]->getDensity(p, _Temperature);
1121         rho2 = _fluides[1]->getDensity(p, _Temperature);
1122         dpi1 = intPressDef(alpha, u_r2, rho1, rho2);
1123         dpi2 = dpi1;
1124         invcsq1 = 1/_fluides[0]->vitesseSonTemperature(_Temperature,rho1);
1125         invcsq1*=invcsq1;
1126         invcsq2 = 1/_fluides[1]->vitesseSonTemperature(_Temperature,rho2);
1127         invcsq2*=invcsq2;
1128
1129         pol_car= Poly.polynome_caracteristique(alpha,  1-alpha, u1_n, u2_n, rho1, rho2, invcsq1, invcsq2, dpi1, dpi2);
1130         for(int ct=0;ct<4;ct++){
1131                 if (abs(pol_car[ct])<_precision*_precision)
1132                         pol_car[ct]=0;
1133         }
1134         vector< complex<double> > vp_right = getRacines(pol_car);
1135         int taille_vp_right = Poly.new_tri_selectif(vp_right,vp_right.size(),_precision);
1136
1137         if(_verbose && _nbTimeStep%_freqSave ==0)
1138         {
1139                 cout<<"Entropic shift right eigenvalues: "<<endl;
1140                 for(unsigned int ct =0; ct<vp_right.size(); ct++)
1141                         cout<<"("<<vp_right[ct].real()<< ", " <<vp_right[ct].imag() <<")";
1142                 cout<< endl;
1143         }
1144         _entropicShift[0] = abs(vp_left[0]-vp_right[0]);
1145         _entropicShift[2] = abs(vp_left[taille_vp_left-1]-vp_right[taille_vp_right-1]);
1146         _entropicShift[1]=0;
1147         for(int i=1;i<min(taille_vp_right-1,taille_vp_left-1);i++)
1148                 _entropicShift[1] = max(_entropicShift[1],abs(vp_left[i]-vp_right[i]));
1149         if(_verbose && _nbTimeStep%_freqSave ==0)
1150         {
1151                 cout<<"eigenvalue jumps "<<endl;
1152                 cout<< _entropicShift[0] << ", " << _entropicShift[1] << ", "<< _entropicShift[2] <<endl;
1153         }
1154 }
1155
1156 void IsothermalTwoFluid::computeScaling(double maxvp)
1157 {
1158         //      double alphaScaling;
1159         //      if(_guessalpha>_precision && _guessalpha<1-_precision)
1160         //              alphaScaling=_guessalpha;
1161         //      else
1162         //              alphaScaling=0.5;
1163
1164         _blockDiag[0]=1;//alphaScaling;
1165         _invBlockDiag[0]=1;//_blockDiag[0];
1166         _blockDiag[1+_Ndim]=1;//-alphaScaling;
1167         _invBlockDiag[1+_Ndim]=1.0;//_blockDiag[1+_Ndim];
1168         for(int q=1; q<_Ndim+1; q++)
1169         {
1170                 _blockDiag[q]=1/(maxvp*maxvp);
1171                 _invBlockDiag[q]=1;//_blockDiag[q];
1172                 _blockDiag[q+1+_Ndim]=1/(maxvp*maxvp);
1173                 _invBlockDiag[q+1+_Ndim]=1;//_blockDiag[q+1+_Ndim];
1174         }
1175 }
1176
1177 void IsothermalTwoFluid::jacobian(const int &j, string nameOfGroup,double * normale)
1178 {
1179         int k;
1180         for(k=0; k<_nVar*_nVar;k++)
1181                 _Jcb[k] = 0;//No implicitation at this stage
1182
1183         // loop on boundaries
1184         if (_limitField[nameOfGroup].bcType==Wall)
1185         {
1186                 for(k=0; k<_nVar;k++)
1187                         _Jcb[k*_nVar + k] = 1;
1188                 for(k=1; k<1+_Ndim;k++)
1189                         for(int l=1; l<1+_Ndim;l++){
1190                                 _Jcb[k*_nVar + l] -= 2*normale[k-1]*normale[l-1];
1191                                 _Jcb[(k+1+_Ndim)*_nVar + l+1+_Ndim] -= 2*normale[k-1]*normale[l-1];
1192                         }
1193         }
1194         //not wall
1195         else if (_limitField[nameOfGroup].bcType==Inlet)
1196         {
1197                 _Jcb[0] = 1;
1198                 _Jcb[(1+_Ndim)*_nVar +1+_Ndim] = 1;
1199                 _Jcb[_nVar]=_limitField[nameOfGroup].v_x[0];
1200                 _Jcb[(2+_Ndim)*_nVar +1+_Ndim] =_limitField[nameOfGroup].v_x[1];
1201                 if(_Ndim>1)
1202                 {
1203                         _Jcb[2*_nVar]=_limitField[nameOfGroup].v_y[0];
1204                         _Jcb[(3+_Ndim)*_nVar +1+_Ndim]= _limitField[nameOfGroup].v_y[1];
1205                         if(_Ndim==3)
1206                         {
1207                                 _Jcb[3*_nVar]=_limitField[nameOfGroup].v_z[0];
1208                                 _Jcb[(4+_Ndim)*_nVar +1+_Ndim]= _limitField[nameOfGroup].v_z[1];
1209
1210                         }
1211                 }
1212         }
1213         // not wall, not inlet
1214         else if (_limitField[nameOfGroup].bcType==Outlet){
1215                 _idm[0] = j*_nVar;
1216                 for(k=1; k<_nVar;k++)
1217                 {_idm[k] = _idm[k-1] + 1;}
1218                 VecGetValues(_conservativeVars, _nVar, _idm, _phi);
1219                 VecGetValues(_primitiveVars, _nVar, _idm, _externalStates);
1220         }
1221         else  if (_limitField[nameOfGroup].bcType!=Neumann && _limitField[nameOfGroup].bcType!=InletPressure)// not wall, not inlet, not outlet
1222         {
1223                 cout << "group named "<<nameOfGroup << " : unknown boundary condition" << endl;
1224                 throw CdmathException("IsothermalTwoFluid::jacobianDiff: This boundary condition is not treated");
1225         }
1226 }
1227
1228 void IsothermalTwoFluid::jacobianDiff(const int &j, string nameOfGroup)
1229 {
1230
1231         int k;
1232         for(k=0; k<_nVar*_nVar;k++)
1233                 _JcbDiff[k] = 0;
1234         if (_limitField[nameOfGroup].bcType==Wall){
1235                 _JcbDiff[0] = 1;
1236                 _JcbDiff[(1+_Ndim)*_nVar +1+_Ndim] = 1;
1237                 _JcbDiff[_nVar]=_limitField[nameOfGroup].v_x[0];
1238                 _JcbDiff[(2+_Ndim)*_nVar +1+_Ndim] =_limitField[nameOfGroup].v_x[1];
1239                 if(_Ndim>1)
1240                 {
1241                         _JcbDiff[2*_nVar]=_limitField[nameOfGroup].v_y[0];
1242                         _JcbDiff[(3+_Ndim)*_nVar +1+_Ndim]= _limitField[nameOfGroup].v_y[1];
1243
1244                         if(_Ndim==3)
1245                         {
1246                                 _JcbDiff[3*_nVar]=_limitField[nameOfGroup].v_z[0];
1247                                 _JcbDiff[(4+_Ndim)*_nVar +1+_Ndim]= _limitField[nameOfGroup].v_z[1];
1248                         }
1249                 }
1250         } else if (_limitField[nameOfGroup].bcType==Inlet){
1251                 /*
1252                 _JcbDiff[0] = 1;
1253                 _JcbDiff[(1+_Ndim)*_nVar +1+_Ndim] = 1;
1254                 _JcbDiff[_nVar]=_limitField[nameOfGroup].v_x[0];
1255                 _JcbDiff[(2+_Ndim)*_nVar +1+_Ndim] =_limitField[nameOfGroup].v_x[1];
1256                 if(_Ndim>1)
1257                 {
1258                         _JcbDiff[2*_nVar]=_limitField[nameOfGroup].v_y[0];
1259                         _JcbDiff[(3+_Ndim)*_nVar +1+_Ndim]= _limitField[nameOfGroup].v_y[1];
1260
1261                         if(_Ndim==3)
1262                         {
1263                                 _JcbDiff[3*_nVar]=_limitField[nameOfGroup].v_z[0];
1264                                 _JcbDiff[(4+_Ndim)*_nVar +1+_Ndim]= _limitField[nameOfGroup].v_z[1];
1265                         }
1266                 }
1267                  */
1268         } else if (_limitField[nameOfGroup].bcType==Outlet){
1269                 /*
1270                 //extraction de l etat courant et primitives
1271                 _idm[0] = j*_nVar;
1272                 for(k=1; k<_nVar;k++)
1273                 {_idm[k] = _idm[k-1] + 1;}
1274                 VecGetValues(_conservativeVars, _nVar, _idm, _phi);
1275                 VecGetValues(_primitiveVars, _nVar, _idm, _externalStates);
1276                  */
1277         }
1278         else if (_limitField[nameOfGroup].bcType!=Neumann && _limitField[nameOfGroup].bcType!=InletPressure){
1279                 cout<<"Condition  limite non traitee pour le bord "<<nameOfGroup<< endl;
1280                 throw CdmathException("IsothermalTwoFluid::jacobianDiff: Condition  limite non traitee");
1281         }
1282 }
1283
1284 void IsothermalTwoFluid::primToCons(const double *P, const int &i, double *W, const int &j){
1285         //P=alpha,p,u1,u2
1286         //W=m1,q1,m2,q2
1287         W[j*_nVar] = P[i*_nVar]*_fluides[0]->getDensity(P[i*_nVar+1],_Temperature);
1288         W[j*_nVar+1+_Ndim] = (1-P[i*_nVar])*_fluides[1]->getDensity(P[i*_nVar+1],_Temperature);
1289         for(int k=0; k<_Ndim; k++)
1290         {
1291                 W[j*_nVar+(k+1)] = W[j*_nVar]*P[i*_nVar+(k+2)];
1292                 W[j*_nVar+(k+1)+1+_Ndim] = W[j*_nVar+1+_Ndim]*P[i*_nVar+(k+2)+_Ndim];
1293         }
1294
1295 }
1296
1297 void IsothermalTwoFluid::consToPrim(const double *Wcons, double* Wprim,double porosity)//To do: treat porosity
1298 {
1299         //P=alpha,p,u1,u2
1300         //W=m1,q1,m2,q2
1301         double m1=Wcons[0];
1302         double m2=Wcons[_Ndim+1];
1303         double e1 = _internalEnergy1;
1304         double e2 = _internalEnergy2;
1305
1306         _minm1=min(m1,_minm1);
1307         _minm2=min(m2,_minm2);
1308         if(m1<-_precision || m2<-_precision)
1309                 _nbMaillesNeg+=1;
1310         if(fabs(m1)<_precision*_precision)
1311         {
1312                 Wprim[0]=0;
1313                 Wprim[1]=_fluides[1]->getPressure(m2*e2,m2);
1314
1315                 for(int idim=0; idim<_Ndim; idim++)
1316                 {
1317                         Wprim[2+_Ndim+idim] = Wcons[2+_Ndim+idim]/Wcons[1+_Ndim];
1318                         Wprim[2+idim] = Wprim[2+_Ndim+idim];
1319                 }
1320         }
1321         else if(fabs(m2)<_precision*_precision)
1322         {
1323                 Wprim[0]=1;
1324                 Wprim[1]=_fluides[0]->getPressure(m1*e1,m1);
1325                 for(int idim=0; idim<_Ndim; idim++)
1326                 {
1327                         Wprim[2+idim] = Wcons[1+idim]/Wcons[0];
1328                         Wprim[2+_Ndim+idim] = Wprim[2+idim];
1329                 }
1330         }
1331         else
1332         {
1333                 for(int idim=0; idim<_Ndim; idim++)
1334                 {
1335                         Wprim[2+idim] = Wcons[1+idim]/Wcons[0];
1336                         Wprim[2+_Ndim+idim] = Wcons[2+_Ndim+idim]/Wcons[1+_Ndim];
1337                 }
1338                 double alphanewton, alphainf=0, alphasup=1;
1339                 int iterMax=50, iter=0;
1340
1341                 double   dp=ecartPression( m1, m2, _guessalpha, e1, e2);
1342                 double   dpprim=ecartPressionDerivee( m1, m2, _guessalpha, e1, e2);
1343
1344                 while(fabs(dp)>1e3*_precision && iter<iterMax)
1345                 {
1346
1347                         //  if (dp>0)
1348                         //              alphainf = _guessalpha;
1349                         //            else
1350                         //              alphansup = _guessalpha;
1351
1352                         //            _guessalpha = (alphainf+alphansup)/2;
1353
1354                         if (dp>0)
1355                                 alphainf = _guessalpha;
1356                         else
1357                                 alphasup = _guessalpha;
1358
1359                         alphanewton = _guessalpha-dp/dpprim;
1360
1361                         if(alphanewton<=alphainf)
1362                         {
1363                                 _guessalpha = (9*alphainf+alphasup)/10;
1364                                 //cout<< "dichotomie"<<endl;
1365                         }
1366                         else if(alphanewton>=alphasup)
1367                         {
1368                                 _guessalpha = (alphainf+9*alphasup)/10;
1369                                 //cout<< "dichotomie"<<endl;
1370                         }
1371                         else
1372                                 _guessalpha=alphanewton;
1373
1374
1375                         if(_verbose && _nbTimeStep%_freqSave ==0)
1376                                 cout<<"consToPrim diphasique iter= " <<iter<<" dp= " << dp<<" dpprim= " << dpprim<< " _guessalpha= " << _guessalpha<<endl;
1377                         dp=ecartPression( m1, m2, _guessalpha, e1, e2);
1378                         dpprim=ecartPressionDerivee( m1, m2, _guessalpha, e1, e2);
1379
1380                         iter++;
1381                 }
1382                 if(_verbose && _nbTimeStep%_freqSave ==0)
1383                         cout<<endl;
1384
1385                 if(iter>=iterMax)
1386                 {
1387                         _err_press_max = max(_err_press_max,fabs(dp/1.e5));
1388                         //            if(_guessalpha>0.5)
1389                         //              _guessalpha=1;
1390                         //            else
1391                         //              _guessalpha=0;
1392                 }
1393                 if(_guessalpha>0.5)
1394                         Wprim[1]=_fluides[0]->getPressure((m1/_guessalpha)*e1,m1/_guessalpha);
1395                 else
1396                         Wprim[1]=_fluides[1]->getPressure((m2/(1-_guessalpha))*e2,m2/(1-_guessalpha));
1397                 Wprim[0]=_guessalpha;
1398         }
1399         if (Wprim[1]<0){
1400                 cout << "pressure = "<< Wprim[1] << " < 0 " << endl;
1401                 cout << "Conservative state = ";
1402                 for(int k=0; k<_nVar; k++){
1403                         cout<<Wcons[k]<<", ";
1404                 }
1405                 cout<<endl;
1406                 *_runLogFile<< "IsothermalTwoFluid::consToPrim: negative pressure = "<< Wprim[1] << " < 0 " << endl;
1407                 throw CdmathException("IsothermalTwoFluid::consToPrim: negative pressure");
1408         }
1409 }
1410
1411 Vector IsothermalTwoFluid::convectionFlux(Vector U,Vector V, Vector normale, double porosity){
1412         if(_verbose){
1413                 cout<<"Ucons"<<endl;
1414                 cout<<U<<endl;
1415                 cout<<"Vprim"<<endl;
1416                 cout<<V<<endl;
1417         }
1418
1419         double phim1=U(0);//phi alpha1 rho1
1420         double phim2=U(1+_Ndim);//phi alpha2 rho2
1421         Vector phiq1(_Ndim),phiq2(_Ndim);//phi alpha1 rho1 u1, phi alpha2 rho2 u2
1422         for(int i=0;i<_Ndim;i++){
1423                 phiq1(i)=U(1+i);
1424                 phiq2(i)=U(2+_Ndim+i);
1425         }
1426         double alpha=V(0);
1427         double pression=V(1);
1428         Vector vitesse1(_Ndim),vitesse2(_Ndim);
1429         for(int i=0;i<_Ndim;i++){
1430                 vitesse1(i)=V(2+i);
1431                 vitesse2(i)=V(2+_Ndim+i);
1432         }
1433
1434         double vitesse1n=vitesse1*normale;
1435         double vitesse2n=vitesse2*normale;
1436
1437         double alpha_roe = _Uroe[0];//Toumi formula
1438         // interfacial pressure term (hyperbolic correction)
1439         double dpi = _Uroe[_nVar];
1440
1441         Vector F(_nVar);
1442         F(0)=phim1*vitesse1n;
1443         F(1+_Ndim)=phim2*vitesse2n;
1444         for(int i=0;i<_Ndim;i++){
1445                 F(1+i)=phim1*vitesse1n*vitesse1(i)+(alpha_roe*pression+dpi*alpha)*porosity*normale(i);
1446                 F(2+_Ndim+i)=phim2*vitesse2n*vitesse2(i)+((1-alpha_roe)*pression-dpi*alpha)*normale(i)*porosity;
1447         }
1448
1449         if(_verbose){
1450                 cout<<"Flux F(U,V)"<<endl;
1451                 cout<<F<<endl;
1452         }
1453
1454         return F;
1455 }
1456
1457 Vector IsothermalTwoFluid::staggeredVFFCFlux()
1458 {
1459         if(_spaceScheme!=staggered || _nonLinearFormulation!=VFFC)
1460                 throw CdmathException("IsothermalTwoFluid::staggeredVFFCFlux: staggeredVFFCFlux method should be called only for VFFC formulation and staggered upwinding");
1461         else//_spaceScheme==staggered
1462         {
1463                 Vector Fij(_nVar);
1464                 double alpha_roe = _Uroe[0];//Toumi formula
1465                 // interfacial pressure term (hyperbolic correction)
1466                 double dpi = _Uroe[_nVar];
1467
1468                 double u1ijn=0, u2ijn=0, phialphaq1n=0, phialphaq2n=0;
1469                 for(int idim=0;idim<_Ndim;idim++){//URoe = alpha, p, u1, u2, dpi
1470                         u1ijn+=_vec_normal[idim]*_Uroe[2+idim];
1471                         u2ijn+=_vec_normal[idim]*_Uroe[2+_Ndim+idim];
1472                 }
1473                 if(u1ijn>=0)
1474                 {
1475                         for(int idim=0;idim<_Ndim;idim++)
1476                                 phialphaq1n+=_vec_normal[idim]*_Ui[1+idim];//phi alpha rho u n
1477                         Fij(0)=phialphaq1n;
1478                         for(int idim=0;idim<_Ndim;idim++)
1479                                 Fij(1+idim)=phialphaq1n*_Vi[2+idim]+(alpha_roe*_Vj[1]*_porosityj+dpi*_Vi[0]*_porosityi)*_vec_normal[idim];
1480                 }
1481                 else
1482                 {
1483                         for(int idim=0;idim<_Ndim;idim++)
1484                                 phialphaq2n+=_vec_normal[idim]*_Uj[1+idim];//phi alpha rho u n
1485                         Fij(0)=phialphaq2n;
1486                         for(int idim=0;idim<_Ndim;idim++)
1487                                 Fij(1+idim)=phialphaq2n*_Vj[2+idim]+(alpha_roe*_Vi[1]*_porosityi+dpi*_Vj[0]*_porosityj)*_vec_normal[idim];
1488                 }
1489
1490                 if(u2ijn>=0)
1491                 {
1492                         for(int idim=0;idim<_Ndim;idim++)
1493                                 phialphaq2n+=_vec_normal[idim]*_Ui[2+_Ndim+idim];//phi alpha rho u n
1494                         Fij(1+_Ndim)=phialphaq2n;
1495                         for(int idim=0;idim<_Ndim;idim++)
1496                                 Fij(2+_Ndim+idim)=phialphaq2n*_Vi[2+_Ndim+idim]+((1-alpha_roe)*_Vj[1]*_porosityj-dpi*_Vi[0]*_porosityi)*_vec_normal[idim];
1497                 }
1498                 else
1499                 {
1500                         for(int idim=0;idim<_Ndim;idim++)
1501                                 phialphaq2n+=_vec_normal[idim]*_Uj[2+_Ndim+idim];//phi alpha rho u n
1502                         Fij(1+_Ndim)=phialphaq2n;
1503                         for(int idim=0;idim<_Ndim;idim++)
1504                                 Fij(2+_Ndim+idim)=phialphaq2n*_Vj[2+_Ndim+idim]+((1-alpha_roe)*_Vi[1]*_porosityi-dpi*_Vj[0]*_porosityj)*_vec_normal[idim];
1505                 }
1506                 return Fij;
1507         }
1508 }
1509
1510 void IsothermalTwoFluid::applyVFRoeLowMachCorrections(bool isBord, string groupname)
1511 {
1512         if(_nonLinearFormulation!=VFRoe)
1513                 throw CdmathException("IsothermalTwoFluid::applyVFRoeLowMachCorrections: applyVFRoeLowMachCorrections method should be called only for VFRoe formulation");
1514         else//_nonLinearFormulation==VFRoe
1515         {
1516                 if(_spaceScheme==lowMach){
1517                         double u1_2=0, u2_2=0;
1518                         for(int i=0;i<_Ndim;i++){
1519                                 u1_2 += _Uroe[2+i]*_Uroe[2+i];
1520                                 u2_2 += _Uroe[2+i+_Ndim]*_Uroe[2+i+_Ndim];
1521                         }
1522
1523                         double  c = _maxvploc;//mixture sound speed
1524                         double M=max(sqrt(u1_2),sqrt(u2_2))/c;//Mach number
1525                         _Vij[1]=M*_Vij[1]+(1-M)*(_Vi[1]+_Vj[1])/2;
1526                         primToCons(_Vij,0,_Uij,0);
1527                 }
1528                 else if(_spaceScheme==pressureCorrection)
1529                 {
1530                         if(_pressureCorrectionOrder>2)
1531                                 throw CdmathException("IsothermalTwoFluid::applyVFRoeLowMachCorrections pressure correction order can be only 1 or 2 for Isothermal two-fluid model");
1532
1533                         double norm_uij=0, uij_n=0, ui_n=0, uj_n=0;//mean velocities
1534                         double rho1 =  _fluides[0]->getDensity(_Uroe[1],_Temperature);
1535                         double rho2 =  _fluides[1]->getDensity(_Uroe[1],_Temperature);
1536                         double m1=_Uroe[0]*rho1,  m2=(1-_Uroe[0])*rho2;
1537                         double rhom=m1+m2;
1538                         for(int i=0;i<_Ndim;i++)
1539                         {
1540                                 norm_uij += (m1*_Uroe[2+i]+m2*_Uroe[2+i+_Ndim])*(m1*_Uroe[2+i]+m2*_Uroe[2+i+_Ndim]);
1541                                 uij_n += (m1*_Uroe[2+i]+m2*_Uroe[2+i+_Ndim])*_vec_normal[i];
1542                                 ui_n += _Vi[2+i]*_vec_normal[i];
1543                                 uj_n += _Vj[2+i]*_vec_normal[i];
1544                         }
1545                         norm_uij=sqrt(norm_uij)/rhom;
1546                         uij_n/=rhom;
1547                         if(norm_uij>_precision)//avoid division by zero
1548                                 _Vij[1]=(_Vi[1]+_Vj[1])/2 + uij_n/norm_uij*(_Vj[1]-_Vi[1])/4 - rhom*norm_uij*(uj_n-ui_n)/4;
1549                         else
1550                                 _Vij[1]=(_Vi[1]+_Vj[1])/2                                    - rhom*norm_uij*(uj_n-ui_n)/4;
1551
1552                 }
1553                 else if(_spaceScheme==staggered)
1554                 {
1555                         double qij_n=0;
1556                         double rho1 =  _fluides[0]->getDensity(_Uroe[1],_Uroe[_nVar-1]);
1557                         double rho2 =  _fluides[1]->getDensity(_Uroe[1],_Uroe[_nVar-1]);
1558                         double m1=_Uroe[0]*rho1,  m2=(1-_Uroe[0])*rho2;
1559                         double rhom=m1+m2;
1560                         for(int i=0;i<_Ndim;i++)
1561                                 qij_n += (m1*_Uroe[2+i]+m2*_Uroe[2+i+_Ndim])*_vec_normal[i];
1562
1563                         if(qij_n>=0){
1564                                 _Vij[0]=_Vi[0];
1565                                 _Vij[1]=_Vj[1];
1566                                 for(int i=0;i<_Ndim;i++)
1567                                 {
1568                                         _Vij[2+i]               =_Vi[2+i];
1569                                         _Vij[2+i+_Ndim] =_Vi[2+i+_Ndim];
1570                                 }
1571                         }
1572                         else{
1573                                 _Vij[0]=_Vj[0];
1574                                 _Vij[1]=_Vi[1];
1575                                 for(int i=0;i<_Ndim;i++)
1576                                 {
1577                                         _Vij[2+i]               =_Vj[2+i];
1578                                         _Vij[2+i+_Ndim] =_Vj[2+i+_Ndim];
1579                                 }
1580                         }
1581                         primToCons(_Vij,0,_Uij,0);
1582                 }
1583         }
1584 }
1585
1586 void IsothermalTwoFluid::testConservation()
1587 {
1588         double SUM, DELTA, x;
1589         int I;
1590         for(int i=0; i<_nVar; i++)
1591         {
1592                 {
1593                         if(i == 0)
1594                                 cout << "Masse totale phase " << 0 <<" (kg): ";
1595                         else if( i == 1+_Ndim)
1596                                 cout << "Masse totale phase " << 1 <<" (kg): ";
1597                         else
1598                         {
1599                                 if(i < 1+_Ndim)
1600                                         cout << "Quantite de mouvement totale phase 0 (kg.m.s^-1): ";
1601                                 else
1602                                         cout << "Quantite de mouvement totale phase 1 (kg.m.s^-1): ";
1603                         }
1604                 }
1605                 SUM = 0;
1606                 DELTA = 0;
1607                 I = i;
1608                 for(int j=0; j<_Nmailles; j++)
1609                 {
1610                         VecGetValues(_old, 1, &I, &x);//on recupere la valeur du champ
1611                         SUM += x*_mesh.getCell(j).getMeasure();
1612                         VecGetValues(_newtonVariation, 1, &I, &x);//on recupere la variation du champ
1613                         DELTA += x*_mesh.getCell(j).getMeasure();
1614                         I += _nVar;
1615                 }
1616                 if(fabs(SUM)>_precision)
1617                         cout << SUM<< ", variation relative: " << fabs(DELTA /SUM)  << endl;
1618                 else
1619                         cout << " a une somme nulle,  variation absolue: " << fabs(DELTA) << endl;
1620         }
1621 }
1622
1623 void IsothermalTwoFluid::save(){
1624         string prim(_path+"/IsothermalTwoFluidPrim_");
1625         string cons(_path+"/IsothermalTwoFluidCons_");
1626         prim+=_fileName;
1627         cons+=_fileName;
1628
1629         PetscInt Ii;
1630         for (long i = 0; i < _Nmailles; i++){
1631                 /* j = 0 : void fraction
1632                            j = 1 : pressure
1633                            j = 2, 3, 4: velocity phase 1
1634                            j = 5, 6, 7: velocity phase 2 */
1635                 for (int j = 0; j < _nVar; j++){
1636                         Ii = i*_nVar +j;
1637                         VecGetValues(_primitiveVars,1,&Ii,&_VV(i,j));
1638                 }
1639         }
1640         if(_saveConservativeField){
1641                 for (long i = 0; i < _Nmailles; i++){
1642                         for (int j = 0; j < _nVar; j++){
1643                                 Ii = i*_nVar +j;
1644                                 //                              cout<<"i= "<<i<< " j= "<<j<<" UU(i,j)= "<<_UU(i,j)<<endl;
1645                                 VecGetValues(_conservativeVars,1,&Ii,&_UU(i,j));
1646                         }
1647                 }
1648                 _UU.setTime(_time,_nbTimeStep);
1649         }
1650         _VV.setTime(_time,_nbTimeStep);
1651         if (_nbTimeStep ==0 || _restartWithNewFileName){
1652                 string prim_suppress ="rm -rf "+prim+"_*";
1653                 string cons_suppress ="rm -rf "+cons+"_*";
1654                 system(prim_suppress.c_str());//Nettoyage des précédents calculs identiques
1655                 system(cons_suppress.c_str());//Nettoyage des précédents calculs identiques
1656                 _VV.setInfoOnComponent(0,"Void_fraction");
1657                 _VV.setInfoOnComponent(1,"Pressure_(Pa)");
1658                 _VV.setInfoOnComponent(2,"Velocity1_x_m/s");
1659                 if (_Ndim>1)
1660                         _VV.setInfoOnComponent(3,"Velocity1_y_m/s");
1661                 if (_Ndim>2)
1662                         _VV.setInfoOnComponent(4,"Velocity1_z_m/s");
1663
1664                 _VV.setInfoOnComponent(2+_Ndim,"Velocity2_x_m/s");
1665                 if (_Ndim>1)
1666                         _VV.setInfoOnComponent(3+_Ndim,"Velocity2_y_m/s");
1667                 if (_Ndim>2)
1668                         _VV.setInfoOnComponent(4+_Ndim,"Velocity2_z_m/s");
1669
1670                 switch(_saveFormat)
1671                 {
1672                 case VTK :
1673                         _VV.writeVTK(prim);
1674                         break;
1675                 case MED :
1676                         _VV.writeMED(prim);
1677                         break;
1678                 case CSV :
1679                         _VV.writeCSV(prim);
1680                         break;
1681                 }
1682
1683                 if(_saveConservativeField){
1684                         _UU.setInfoOnComponent(0,"Partial_density1");// (kg/m^3)
1685                         _UU.setInfoOnComponent(1,"Momentum1_x");// phase1  (kg/m^2/s)
1686                         if (_Ndim>1)
1687                                 _UU.setInfoOnComponent(2,"Momentum1_y");// phase1 (kg/m^2/s)
1688                         if (_Ndim>2)
1689                                 _UU.setInfoOnComponent(3,"Momentum1_z");// phase1 (kg/m^2/s)
1690
1691                         _UU.setInfoOnComponent(1+_Ndim,"Partial_density2");// phase2 (kg/m^3)
1692                         _UU.setInfoOnComponent(2+_Ndim,"Momentum2_x");// phase2 (kg/m^2/s)
1693                         if (_Ndim>1)
1694                                 _UU.setInfoOnComponent(3+_Ndim,"Momentum2_y");// phase2 (kg/m^2/s)
1695                         if (_Ndim>2)
1696                                 _UU.setInfoOnComponent(4+_Ndim,"Momentum2_z");// phase2 (kg/m^2/s)
1697
1698                         switch(_saveFormat)
1699                         {
1700                         case VTK :
1701                                 _UU.writeVTK(cons);
1702                                 break;
1703                         case MED :
1704                                 _UU.writeMED(cons);
1705                                 break;
1706                         case CSV :
1707                                 _UU.writeCSV(cons);
1708                                 break;
1709                         }
1710                 }
1711         }
1712         else{
1713                 switch(_saveFormat)
1714                 {
1715                 case VTK :
1716                         _VV.writeVTK(prim,false);
1717                         break;
1718                 case MED :
1719                         _VV.writeMED(prim,false);
1720                         break;
1721                 case CSV :
1722                         _VV.writeCSV(prim);
1723                         break;
1724                 }
1725
1726                 if(_saveConservativeField){
1727                         switch(_saveFormat)
1728                         {
1729                         case VTK :
1730                                 _UU.writeVTK(cons,false);
1731                                 break;
1732                         case MED :
1733                                 _UU.writeMED(cons,false);
1734                                 break;
1735                         case CSV :
1736                                 _UU.writeCSV(cons);
1737                                 break;
1738                         }
1739                 }
1740         }
1741         if(_saveVelocity){
1742                 for (long i = 0; i < _Nmailles; i++){
1743                         // j = 0 : concentration, j=1 : pressure; j = _nVar - 1: temperature; j = 2,..,_nVar-2: velocity
1744                         for (int j = 0; j < _Ndim; j++)//On récupère les composantes de vitesse
1745                         {
1746                                 Ii = i*_nVar +2+j;
1747                                 VecGetValues(_primitiveVars,1,&Ii,&_Vitesse1(i,j));
1748                                 Ii=i*_nVar +2+j+_Ndim;
1749                                 VecGetValues(_primitiveVars,1,&Ii,&_Vitesse2(i,j));
1750                         }
1751                         for (int j = _Ndim; j < 3; j++){//On met à zero les composantes de vitesse si la dimension est <3
1752                                 _Vitesse1(i,j)=0;
1753                                 _Vitesse2(i,j)=0;
1754                         }
1755                 }
1756                 _Vitesse1.setTime(_time,_nbTimeStep);
1757                 _Vitesse2.setTime(_time,_nbTimeStep);
1758                 if (_nbTimeStep ==0 || _restartWithNewFileName){
1759                         _Vitesse1.setInfoOnComponent(0,"Velocity_x_(m/s)");
1760                         _Vitesse1.setInfoOnComponent(1,"Velocity_y_(m/s)");
1761                         _Vitesse1.setInfoOnComponent(2,"Velocity_z_(m/s)");
1762
1763                         _Vitesse2.setInfoOnComponent(0,"Velocity_x_(m/s)");
1764                         _Vitesse2.setInfoOnComponent(1,"Velocity_y_(m/s)");
1765                         _Vitesse2.setInfoOnComponent(2,"Velocity_z_(m/s)");
1766
1767                         switch(_saveFormat)
1768                         {
1769                         case VTK :
1770                                 _Vitesse1.writeVTK(prim+"_GasVelocity");
1771                                 _Vitesse2.writeVTK(prim+"_LiquidVelocity");
1772                                 break;
1773                         case MED :
1774                                 _Vitesse1.writeMED(prim+"_GasVelocity");
1775                                 _Vitesse2.writeMED(prim+"_LiquidVelocity");
1776                                 break;
1777                         case CSV :
1778                                 _Vitesse1.writeCSV(prim+"_GasVelocity");
1779                                 _Vitesse2.writeCSV(prim+"_LiquidVelocity");
1780                                 break;
1781                         }
1782                 }
1783                 else{
1784                         switch(_saveFormat)
1785                         {
1786                         case VTK :
1787                                 _Vitesse1.writeVTK(prim+"_GasVelocity",false);
1788                                 _Vitesse2.writeVTK(prim+"_LiquidVelocity",false);
1789                                 break;
1790                         case MED :
1791                                 _Vitesse1.writeMED(prim+"_GasVelocity",false);
1792                                 _Vitesse2.writeMED(prim+"_LiquidVelocity",false);
1793                                 break;
1794                         case CSV :
1795                                 _Vitesse1.writeCSV(prim+"_GasVelocity");
1796                                 _Vitesse2.writeCSV(prim+"_LiquidVelocity");
1797                                 break;
1798                         }
1799                 }
1800         }
1801
1802         if (_restartWithNewFileName)
1803                 _restartWithNewFileName=false;
1804 }
1805