SALOME platform Git repositories - tools/solverlab.git/blob

   1 import cdmath
   2 import WaveSystemUpwind
   3 import matplotlib
   4 matplotlib.use("Agg")
   5 import matplotlib.pyplot as plt
   6 import numpy as np
   7 from math import log10, sqrt
   8 import sys
   9 import time, json
  10
  11
  12 def test_validation2DWaveSystemUpwindSquares(bctype,scaling):
  13     start = time.time()
  14     #### 2D square mesh
  15     meshList=[7,15,31,51,81]#,101
  16     #meshList=['squareWithSquares_1','squareWithSquares_2','squareWithSquares_3','squareWithSquares_4','squareWithSquares_5']
  17     mesh_path='../../../ressources/2DCartesien/'
  18     meshType="Regular squares"
  19     testColor="Green"
  20     nbMeshes=len(meshList)
  21     error_p_tab=[0]*nbMeshes
  22     error_u_tab=[0]*nbMeshes
  23     mesh_size_tab=[0]*nbMeshes
  24     mesh_name='squareWithSquares'
  25     diag_data_press=[0]*nbMeshes
  26     diag_data_vel=[0]*nbMeshes
  27     time_tab=[0]*nbMeshes
  28     t_final=[0]*nbMeshes
  29     ndt_final=[0]*nbMeshes
  30     max_vel=[0]*nbMeshes
  31     resolution=100
  32     curv_abs=np.linspace(0,sqrt(2),resolution+1)
  33
  34     plt.close('all')
  35     i=0
  36     cfl=0.5
  37     # Storing of numerical errors, mesh sizes and diagonal values
  38     #for filename in meshList:
  39     for nx in meshList:
  40         my_mesh=cdmath.Mesh(0,1,nx,0,1,nx)
  41         error_p_tab[i], error_u_tab[i], mesh_size_tab[i], t_final[i], ndt_final[i], max_vel[i], diag_data_press[i], diag_data_vel[i], time_tab[i] =WaveSystemUpwind.solve(my_mesh,"square"+str(nx)+'x'+str(nx), resolution,scaling,meshType,testColor,cfl,bctype)
  42         #error_p_tab[i], error_u_tab[i], mesh_size_tab[i], t_final[i], ndt_final[i], max_vel[i], diag_data_press[i], diag_data_vel[i], time_tab[i] =WaveSystemUpwind.solve_file(mesh_path+filename, mesh_name, resolution,scaling,meshType,testColor,cfl,bctype)
  43         assert max_vel[i]>0.0001 and max_vel[i]<1.
  44         print( "error_p_tab[i]=", error_p_tab[i], " zero leads to singularity in plotting of convergence curve")
  45         #error_p_tab[i]=log10(error_p_tab[i])
  46         error_u_tab[i]=log10(error_u_tab[i])
  47         time_tab[i]=log10(time_tab[i])
  48         i=i+1
  49
  50     end = time.time()
  51
  52     # Plot over diagonal line
  53     for i in range(nbMeshes):
  54         plt.plot(curv_abs, diag_data_press[i], label= str(mesh_size_tab[i]) + ' cells')
  55     plt.legend()
  56     plt.xlabel('Position on diagonal line')
  57     plt.ylabel('Pressure on diagonal line')
  58     plt.title('Plot over diagonal line for stationary wave system \n with upwind scheme on 2D square meshes')
  59     plt.savefig(mesh_name+'_Pressure_2DWaveSystemUpwind_'+"PlotOverDiagonalLine.png")
  60     plt.close()
  61
  62     plt.clf()
  63     for i in range(nbMeshes):
  64         plt.plot(curv_abs, diag_data_vel[i],   label= str(mesh_size_tab[i]) + ' cells')
  65     plt.legend()
  66     plt.xlabel('Position on diagonal line')
  67     plt.ylabel('Velocity on diagonal line')
  68     plt.title('Plot over diagonal line for the stationary wave system \n with upwind scheme on 2D square meshes')
  69     plt.savefig(mesh_name+"_Velocity_2DWaveSystemUpwind_"+"PlotOverDiagonalLine.png")
  70     plt.close()
  71
  72     # Plot of number of time steps
  73     plt.close()
  74     plt.plot(mesh_size_tab, ndt_final, label='Number of time step to reach stationary regime')
  75     plt.legend()
  76     plt.xlabel('number of cells')
  77     plt.ylabel('Max time steps for stationary regime')
  78     plt.title('Number of times steps required for the stationary Wave System \n with upwind scheme on 2D square meshes')
  79     plt.savefig(mesh_name+"_2DWaveSystemUpwind_"+"TimeSteps.png")
  80
  81     # Plot of stationary time
  82     plt.close()
  83     plt.plot(mesh_size_tab, t_final, label='Time where stationary regime is reached')
  84     plt.legend()
  85     plt.xlabel('number of cells')
  86     plt.ylabel('Max time for stationary regime')
  87     plt.title('Simulated time  for the stationary Wave System \n with upwind scheme on 2D square meshes')
  88     plt.savefig(mesh_name+"_2DWaveSystemUpwind_"+"TimeFinal.png")
  89
  90     # Plot of number of maximal velocity norm
  91     plt.close()
  92     plt.plot(mesh_size_tab, max_vel, label='Maximum velocity norm')
  93     plt.legend()
  94     plt.xlabel('number of cells')
  95     plt.ylabel('Max velocity norm')
  96     plt.title('Maximum velocity norm  for the stationary Wave System \n with upwind scheme on 2D square meshes')
  97     plt.savefig(mesh_name+"_2DWaveSystemUpwind_"+"MaxVelNorm.png")
  98
  99     for i in range(nbMeshes):
 100         mesh_size_tab[i]=0.5*log10(mesh_size_tab[i])
 101
 102     # Least square linear regression
 103     # Find the best a,b such that f(x)=ax+b best approximates the convergence curve
 104     # The vector X=(a,b) solves a symmetric linear system AX=B with A=(a1,a2\\a2,a3), B=(b1,b2)
 105     a1=np.dot(mesh_size_tab,mesh_size_tab)
 106     a2=np.sum(mesh_size_tab)
 107     a3=nbMeshes
 108
 109     det=a1*a3-a2*a2
 110     assert det!=0, 'test_validation2DWaveSystemUpwind_squares() : Make sure you use distinct meshes and at least two meshes'
 111
 112     #zero pressure leads to singularity
 113     # b1p=np.dot(error_p_tab,mesh_size_tab)
 114     # b2p=np.sum(error_p_tab)
 115     # ap=( a3*b1p-a2*b2p)/det
 116     # bp=(-a2*b1p+a1*b2p)/det
 117
 118     # print("FV upwind on 2D square meshes : scheme order for pressure is ", -ap)
 119
 120     b1u=np.dot(error_u_tab,mesh_size_tab)
 121     b2u=np.sum(error_u_tab)
 122     au=( a3*b1u-a2*b2u)/det
 123     bu=(-a2*b1u+a1*b2u)/det
 124
 125     print("FV upwind on 2D square meshes : scheme order for velocity is ", -au)
 126
 127     # Plot of convergence curves
 128     # plt.close()
 129     # plt.plot(mesh_size_tab, error_p_tab, label='|error on stationary pressure|')
 130     # plt.legend()
 131     # plt.xlabel('1/2 log(number of cells)')
 132     # plt.ylabel('|error p|')
 133     # plt.title('Convergence of finite volumes for the stationary Wave System \n with upwind scheme on 2D square meshes')
 134     # plt.savefig(mesh_name+"_Pressure_2DWaveSystemUpwind_"+"ConvergenceCurve.png")
 135
 136     plt.close()
 137     plt.plot(mesh_size_tab, error_u_tab, label='log(|error on stationary velocity|)')
 138     plt.legend()
 139     plt.xlabel('1/2 log(number of cells)')
 140     plt.ylabel('log(|error u|)')
 141     plt.title('Convergence of finite volumes for the stationary Wave System\n with upwind scheme  on 2D square meshes')
 142     plt.savefig(mesh_name+"_Velocity_2DWaveSystemUpwind_"+"ConvergenceCurve.png")
 143
 144     # Plot of computational time
 145     plt.close()
 146     plt.plot(mesh_size_tab, time_tab, label='log(cpu time)')
 147     plt.legend()
 148     plt.xlabel('1/2 log(number of cells)')
 149     plt.ylabel('log(cpu time)')
 150     plt.title('Computational time of finite volumes for the stationary Wave System \n with upwind scheme on 2D square meshes')
 151     plt.savefig(mesh_name+"_2DWaveSystemUpwind_ComputationalTimeSquares.png")
 152
 153     plt.close('all')
 154
 155     convergence_synthesis={}
 156
 157     convergence_synthesis["PDE_model"]="Wave system"
 158     convergence_synthesis["PDE_is_stationary"]=False
 159     convergence_synthesis["PDE_search_for_stationary_solution"]=True
 160     convergence_synthesis["Numerical_method_name"]="Upwind"
 161     convergence_synthesis["Numerical_method_space_discretization"]="Finite volumes"
 162     convergence_synthesis["Numerical_method_time_discretization"]="Implicit"
 163     convergence_synthesis["Initial_data"]="Constant pressure, divergence free velocity"
 164     convergence_synthesis["Boundary_conditions"]="Periodic"
 165     convergence_synthesis["Numerical_parameter_cfl"]=cfl
 166     convergence_synthesis["Space_dimension"]=2
 167     convergence_synthesis["Mesh_dimension"]=2
 168     convergence_synthesis["Mesh_names"]=meshList
 169     convergence_synthesis["Mesh_type"]=meshType
 170     convergence_synthesis["Mesh_path"]=mesh_path
 171     convergence_synthesis["Mesh_description"]=mesh_name
 172     convergence_synthesis["Mesh_sizes"]=mesh_size_tab
 173     convergence_synthesis["Mesh_cell_type"]="Squares"
 174     convergence_synthesis["Numerical_error_velocity"]=error_u_tab
 175     convergence_synthesis["Numerical_error_pressure"]=error_p_tab
 176     convergence_synthesis["Max_vel_norm"]=max_vel
 177     convergence_synthesis["Final_time"]=t_final
 178     convergence_synthesis["Final_time_step"]=ndt_final
 179     convergence_synthesis["Scheme_order"]=-au#min(-au,-ap)
 180     convergence_synthesis["Scheme_order_vel"]=-au
 181     #convergence_synthesis["Scheme_order_press"]=-ap
 182     convergence_synthesis["Scaling_preconditioner"]="None"
 183     convergence_synthesis["Test_color"]=testColor
 184     convergence_synthesis["Computational_time"]=end-start
 185
 186     with open('Convergence_WaveSystem_2DFV_Upwind_'+mesh_name+'.json', 'w') as outfile:
 187         json.dump(convergence_synthesis, outfile)
 188
 189 if __name__ == """__main__""":
 190     if len(sys.argv) >2 :
 191         bctype = sys.argv[1]
 192         scaling = int(sys.argv[2])
 193         test_validation2DWaveSystemUpwindSquares(bctype,scaling)
 194     else :
 195         raise ValueError("test_validation2DWaveSystemUpwindSquares.py expects a mesh file name and a scaling parameter")