Initial Commit

Readme.md

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+
+
+```python
+from fenics import *
+from dolfin import *
+import mshr
+import matplotlib.pyplot as plt
+import numpy as np
+```
+
+
+```python
+T = 60*60*5 #final step
+num_steps = 50
+dt = T/num_steps #step size
+```
+
+
+```python
+#2 Create mesh and define function space
+domain = mshr.Circle(Point(0.,0.),1.0,60)
+mesh = mshr.generate_mesh(domain, 25)
+V = FunctionSpace(mesh, 'Lagrange', 1) #Lagrange are triangular elements
+plot(mesh)
+plt.show()
+```
+
+
+![png](output_2_0.png)
+
+
+
+```python
+#3 Defining boundary conditions (Dirichlet)
+D = 1.4E-7 #cm^2/s
+u_D = Constant(0.1)
+
+def Dirichlet_boundary(x, on_boundary):
+    return on_boundary 
+
+bc = DirichletBC(V, Constant(1), Dirichlet_boundary)
+```
+
+
+```python
+#Defining initial values and variational problem
+u_n = interpolate(u_D,V)
+
+u = TrialFunction(V)
+v = TestFunction(V)
+f = Constant(0)
+
+F = u*v*dx+D*dt*dot(grad(u), grad(v))*dx-(u_n+dt*f)*v*dx
+a, L = lhs(F), rhs(F)
+```
+
+
+```python
+#Resolution on time steps
+u = Function(V)
+t = 0
+
+vtkfile = File('sol/solution.pvd')
+for n in range(num_steps):
+    #update current time
+    t += dt
+    u_D.t = t
+    #compute solution
+    solve(a==L, u, bc)
+    #vtkfile << (u,t)
+    plot(u)
+    plt.show()
+    #update previous solution
+    u_n.assign(u)
+```
+
+
+![png](output_5_0.png)
+
+
+![png](output_5_48.png)