Questions tagged [diffusion]

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26
votes
1answer
5k 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)...
27
votes
2answers
5k views

Is Crank-Nicolson a stable discretization scheme for Reaction-Diffusion-Advection (convection) equation?

I am not very familiar with the common discretization schemes for PDEs. I know that Crank-Nicolson is popular scheme for discretizing the diffusion equation. Is also a good choice for the advection ...
4
votes
1answer
285 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 ...
3
votes
2answers
833 views

Molecular Dynamics: Diffusion with PBC

How can I implement the computation of the diffusion coefficient $D$ using periodic boundary conditions (PBC)? I use molecular dynamics of a set of $nboby$ particles with positions $pos(3,nbody)$ in ...
2
votes
2answers
451 views

Neumann boundary conditions diffusion equations methods of lines

I want to solve the diffusion equation using the method of lines with Neumann boundary conditions $$ \frac{\partial p}{\partial t}=\frac{\partial^2p}{\partial x^2}\\ \frac{\partial p}{\partial x}(x=0)=...
6
votes
1answer
168 views

Can heat distribution in an optical element irradiated by laser be oscillating?

I am modelling a heat distribution in optical element irradiated by laser. System is radially symmetric, and element is thin, i.e. heat value depends only on distance from center. Heat is received via ...
4
votes
1answer
2k views

Numerical solution of non-linear diffusion equation via finite-difference with the Crank-Nicolson method

I want to numerically solve the non-linear diffusion equation: $$ \frac{\partial}{\partial t} T(x,t)= \frac{\partial}{\partial x}\left(T^{5/2} \frac{\partial T}{\partial x} \right) $$ I want to use ...
3
votes
1answer
185 views

Solving the heat diffusion equation with source term

I am trying to solve the 1-D heat equation numerically with a variable source term. The system is basically a tank containing styrene in which it polymerizes to liberate heat. I have assumed that the ...
1
vote
1answer
103 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 ...
0
votes
0answers
70 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 ...