analytical solution rewriting

euler_error/linear_growth_euler_errors.py

@@ -7,13 +7,13 @@
 import numpy as np
 import numpy as np
 import dolfin as df
 import dolfin as df
 import matplotlib.pyplot as plt
 import matplotlib.pyplot as plt
-import progressbar
+# import progressbar
 from scipy.optimize import curve_fit
 from scipy.optimize import curve_fit
 
 
 df.set_log_level(df.LogLevel.ERROR)
 df.set_log_level(df.LogLevel.ERROR)
 df.parameters['form_compiler']['optimize'] = True
 df.parameters['form_compiler']['optimize'] = True
 
 
-def advection_diffusion(Nx, L, Nt, tmax, v, D):
+def advection_diffusion(Nx, L, Nt, tmax, v, D, m):
     # mesh, function space, function, test function
     # mesh, function space, function, test function
     mesh = df.IntervalMesh(Nx, 0, L)
     mesh = df.IntervalMesh(Nx, 0, L)
     function_space = df.FunctionSpace(mesh, 'P', 1)
     function_space = df.FunctionSpace(mesh, 'P', 1)
@@ -37,7 +37,7 @@ def advection_diffusion(Nx, L, Nt, tmax, v, D):
             + df.inner((u * c0).dx(0), tc)
             + df.inner((u * c0).dx(0), tc)
             + D * df.inner(tc.dx(0), c.dx(0))) * df.dx(mesh)
             + D * df.inner(tc.dx(0), c.dx(0))) * df.dx(mesh)
 
 
-    for i in progressbar.progressbar(range(1, len(times))):
+    for i in range(1, len(times)):
         v.t = times[i]
         v.t = times[i]
         u.assign(df.project(v, function_space))
         u.assign(df.project(v, function_space))
         df.solve(form == 0, c)
         df.solve(form == 0, c)
@@ -49,15 +49,15 @@ def advection_diffusion(Nx, L, Nt, tmax, v, D):
 
 
     return [c_array,x_array]
     return [c_array,x_array]
 
 
-Nx, L, tmax, D, b, m = 100, 1, 1, 0.1, 0.01, 2
+Nx, L, tmax, D, b, m = 100, 0.1, 1, 0.1, 0.01, 2
 v = df.Expression('b*x[0]/(L + b*t)', b=b, L=L, t=0, degree=1)
 v = df.Expression('b*x[0]/(L + b*t)', b=b, L=L, t=0, degree=1)
-Nt_array = np.array([5, 10, 15, 20, 25, 30])
+Nt_array = np.array([10, 20, 30, 40, 50, 60, 70, 80, 90, 100])
 # , 400, 800, 1600, 3200, 6400, 12800])
 # , 400, 800, 1600, 3200, 6400, 12800])
 dt_array = tmax/(Nt_array)
 dt_array = tmax/(Nt_array)
 error_in_c = np.zeros(len(Nt_array))
 error_in_c = np.zeros(len(Nt_array))
 
 
 for i in range(len(Nt_array)):
 for i in range(len(Nt_array)):
-    c, x = advection_diffusion(Nx, L, Nt_array[i], tmax, v, D)
+    c, x = advection_diffusion(Nx, L, Nt_array[i], tmax, v, D, m)
     times = np.linspace(0, tmax, Nt_array[i]+1)
     times = np.linspace(0, tmax, Nt_array[i]+1)
     c_exact = np.zeros((Nt_array[i]+1, Nx+1))
     c_exact = np.zeros((Nt_array[i]+1, Nx+1))
     for j in range(0, Nt_array[i]+1):
     for j in range(0, Nt_array[i]+1):