All Questions
24
questions
0
votes
0
answers
109
views
Solving a steady-state PDE
I'm working on trying to solve a steady state PDE in python and I am quite new to python and I am slightly confused on the implementation details. I have an example implementation of solving a non-...
- 43
3
votes
0
answers
158
views
Form of nonlinear diffusion equation
Consider the following nonlinear diffusion problem,
$$
\frac{\partial u}{\partial t} = x^{-2}\frac{\partial}{\partial x}\left(x^2 u^4 \frac{\partial u}{\partial x}\right), \quad 0 < x < 1
$$
We ...
- 617
4
votes
0
answers
241
views
Spurious oscillations in solving diffusion problems using finite elements
I've been struggling with this problem for a while so I hope someone can help me here.
I'm trying to solve the McNabb-Foster equations for hydrogen diffusion in metals using a simple 1D finite element ...
- 41
2
votes
3
answers
178
views
Should reaction be taken into account in the CFL condition when solving advection-diffusion-reaction equations numerically?
I'm dealing with the numerical resolution of advection-diffusion-reaction equations.
I've encountered references on CFL conditions for conservation laws as well as advection-diffusion equations.
I'm ...
- 61
3
votes
0
answers
121
views
Strange Picard iteration
I am interested in solving the equation
$$
\begin{aligned} \nabla \cdot\left(\nabla \phi-\frac{\nabla \phi}{|\nabla \phi|}\right) &=0 & & \text { in } \Omega \\ \phi &=0 & & \...
- 601
1
vote
0
answers
62
views
How to achieve (approx) unit scaling of a non-linear diffusion (heat) equation with a wildly varying diffusion coefficient?
I have numerical issues with a poorly scaled one-dimensional non-linear diffusion equation in physical co-ordinates
$$ \frac{\partial{u}}{\partial{t}}(x,t) = \frac{\partial}{\partial{x}}\left(D(u) \...
-1
votes
1
answer
437
views
Simulating 1D diffusion
I'm trying to understand the influence of Neumann boundary condition while simulating 1D diffusion equation
$$
\frac{\partial C}{\partial t} = \nabla \cdot (D \nabla C).
$$
The initial value is set ...
- 433
0
votes
0
answers
82
views
Comparison of diffusion time - theoretical value vs computed
This is a follow up to my previous post
I've been trying to compare the diffusion time obtained from theoretical
derivation(answered in my previous post) and what is obtained computationally, for a ...
- 433
4
votes
1
answer
365
views
Computation of diffusion time
While simulating the diffusion of a substance in 1D,
$$
\frac{\partial C}{\partial t} = \nabla \cdot (D \nabla C).
$$
I'd like to compute the diffusion time
In this link, the diffusion time is given ...
- 433
3
votes
0
answers
110
views
How to account for the interface between two different phases in a discretized diffusion model?
I have tried to set up a model for the diffusion of a gas into a liquid. The two media are next to each other and the geometry is spherical because the system should simulate the diffusion out of a ...
- 91
1
vote
0
answers
139
views
Hello word in FEniCS? [closed]
I am trying to start using FEniCS, but have a problem with the simple hello world examples given in the books. Could you please give me the simplest hello world ...
- 11
0
votes
2
answers
558
views
Stable implicit method to solve convection-heat diffusion in 3D
The last couple of hours I have been looking for an unconditionally stable method to solve the convection-diffusion equation within a 3D inhomogeneous material.
Here's the well known diffusion-...
- 146
0
votes
0
answers
251
views
Reaction-diffusion equations
I'm simulating a biological phenomena with reaction diffusion equations. There are multiple diffusing materials and there are some complex relations about consumption and production of such materials. ...
- 9
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
0
answers
214
views
Discontinuity at Interface
The equation at the left of the interface is
\begin{equation}
\displaystyle\frac{\partial C_i}{\partial t} = D_i \nabla^2 C_i - z_i \frac{D_i}{RT}F \nabla \cdot (C_i \nabla \phi_2)
\end{equation}
...
- 183