All Questions
Tagged with crank-nicolson diffusion
6
questions
1
vote
1
answer
366
views
Crank Nicolson Method with closed boundary conditions
I want to simulate 1D diffusion with a constant diffusion coefficient using the Crank-Nicolson method.
$$\frac{\partial u (x,t)}{\partial t} = D \frac{\partial^2 u(x,t)}{\partial x^2}.$$
I take an ...
- 111
1
vote
1
answer
323
views
Crank-Nicholson for diffusion-advection vs diffusion equation
Let's consider the following 1D diffusion equation:
$\frac{\partial u}{\partial t} = xk \frac{\partial}{\partial x}(\frac{1}{x}\frac{\partial u}{\partial x})$
where we assume that the diffusion ...
- 172
6
votes
2
answers
389
views
Is the diffusion equation with Neumann and Dirichlet BCs well-posed?
I am considering the following diffusion equation:
$$\frac{\partial f}{\partial t} = \frac{\partial}{\partial x}[D(x,t)\frac{\partial f}{\partial x}]$$
over a grid ...
- 171
6
votes
2
answers
237
views
Is this system of diffusion equations well-posed?
I’m using a standard Crank-Nicholson algorithm to solve this system of two coupled diffusion equations:
$$\dot{u} - \dot{v} = \frac{\partial}{\partial x} \left( \alpha(x) \frac{\partial u}{\partial x}...
user20536
1
vote
1
answer
409
views
Numerical Solution of non-linear diffusion equation using Finite Differencing
I'm trying to solve the following non-linear diffusion equation:
$$
\frac{\partial}{\partial t} u(x,t)= \frac{\partial^{2}}{\partial x^{2}}u(x,t)^{3}$$ $$ -1\leq x \leq1, t \geq 0
$$ with the boundary ...
- 113
29
votes
1
answer
7k
views
Conservation of a physical quantity when using Neumann boundary conditions applied to the advection-diffusion equation
I don't understand the different behaviour of the advection-diffusion equation when I apply different boundary conditions. My motivation is the simulation of a real physical quantity (particle density)...
- 5,429