# 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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 ...