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Both models Working

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@ -4,7 +4,7 @@
#1 Loading functions and modules #1 Loading functions and modules
from fenics import * from fenics import *
import matplotlib.pyplot as plt import matplotlib.pyplot as plt
T = 2.0
T = 0.1
num_steps = 20 num_steps = 20
dt = T/num_steps dt = T/num_steps
rho = 7500 rho = 7500
@ -49,143 +49,135 @@ F = u*v*dx + alpha*dt*dot(grad(u), grad(v))*dx-u_n*v*dx
a, L = lhs(F), rhs(F) a, L = lhs(F), rhs(F)
``` ```
Calling FFC just-in-time (JIT) compiler, this may take some time.
```python ```python
vtkfile = File('solution/solution.pvd')
u = Function(V) u = Function(V)
t = 0 t = 0
for n in range(num_steps): for n in range(num_steps):
t += dt t += dt
#u0.t = t #u0.t = t
solve(a == L, u, bc) solve(a == L, u, bc)
c = plot(u,)
plt.colorbar(c)
plt.show()
#c = plot(u,)
#plt.colorbar(c)
#plt.show()
####
vtkfile << (u, t)
u_n.assign(u) u_n.assign(u)
``` ```
Calling FFC just-in-time (JIT) compiler, this may take some time.
![png](output_4_1.png)
![png](output_4_2.png)
![png](output_4_3.png)
![png](output_4_4.png)
![png](output_4_5.png)
![png](output_4_6.png)
![png](output_4_7.png)
![png](output_4_8.png)
![png](output_4_9.png)
```python
1E-13
```
![png](output_4_10.png)
![png](output_4_11.png)
1e-13
![png](output_4_12.png)
```python
1e2
```
![png](output_4_13.png)
100.0
![png](output_4_14.png)
![png](output_4_15.png)
```python
1E-13+1e2
```
![png](output_4_16.png)
100.0000000000001
![png](output_4_17.png)
# Boundary conditions
![png](output_4_18.png)
```python
#1 Loading functions and modules
from fenics import *
import matplotlib.pyplot as plt
T = 4
num_steps = 200
dt = T/num_steps
rho = 7500
Cp = 500
k = 50
alpha = k/(rho*Cp)
```
```python
#2 Create mesh and define function space
nx = 0.008
ny = 0.003
mesh = RectangleMesh(Point(0,0),Point(nx,ny),8, 8,'left')
V = FunctionSpace(mesh, 'Lagrange', 1) #Lagrange are triangular elements
plot(mesh)
plt.show()
![png](output_4_19.png)
```
![png](output_4_20.png)
![png](output_10_0.png)
```python ```python
1E-7
```
#Boundary Conditions
tol = 1E-14
1e-07
def BC1(x, on_boundary):
return on_boundary and abs(x[0]-nx) < tol
def BC2(x, on_boundary):
return on_boundary and abs(x[0]-0) < tol
bc1=DirichletBC(V,Constant(25),BC1)
bc2=DirichletBC(V,Constant(800),BC2)
bc=(bc1,bc2)
```
```python ```python
1e2
u_n = project(25, V)
u = TrialFunction(V)
v = TestFunction(V)
f = Constant(0.0)
F = u*v*dx + alpha*dt*dot(grad(u), grad(v))*dx-u_n*v*dx
a, L = lhs(F), rhs(F)
``` ```
100.0
```python ```python
1E-7+1e2
vtkfile = File('solution/solution2.pvd')
u = Function(V)
t = 0
for n in range(num_steps):
t += dt
#u0.t = t
solve(a == L, u, bc)
vtkfile << (u, t)
#c = plot(u,)
#plt.colorbar(c)
#plt.show()
u_n.assign(u)
``` ```
100.0000001
```python ```python
``` ```

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solution/solution2000073.vtu View File

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