# Questions tagged [diffusion]

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### 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)...
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### 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 ...
319 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 ...
859 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 ...
639 views

I want to solve the diffusion equation using the method of lines with Neumann boundary conditions $$\frac{\partial p}{\partial t}=\frac{\partial^2p}{\partial x^2}\\ \frac{\partial p}{\partial x}(x=0)=... 0answers 73 views ### Comparison of diffusion time - theoretical value vs computed This is a follow up to my previous post I've been trying to compare the diffusion time obtained from theoretical derivation(answered in my previous post) and what is obtained computationally, for a ... 1answer 170 views ### Can heat distribution in an optical element irradiated by laser be oscillating? I am modelling a heat distribution in optical element irradiated by laser. System is radially symmetric, and element is thin, i.e. heat value depends only on distance from center. Heat is received via ... 1answer 2k views ### Numerical solution of non-linear diffusion equation via finite-difference with the Crank-Nicolson method I want to numerically solve the non-linear diffusion equation:$$ \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 ...
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 ...