Questions tagged [diffusion]

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4
votes
1answer
203 views

The most efficient way to solve diffusion equation with concentrated initial condition

I want to solve the diffusion equation, i.e. $$ \dot{f} - f'' = 0 $$ with a boundary condition $f(0) = f(1) = 0$ and with an initial condition that $f$ is a boxcar function concentrated over some ...
1
vote
0answers
50 views

Calculating the number of molecules diffusing out of a volume [closed]

I have a system of reactions that are governed by differential equations. They are reacting inside of a volume with known dimensions i.e lbh. I don't have any other information on their position ...
0
votes
1answer
112 views

max speed <--> time discretization

I'm working on a heat diffusion problem, $$ \frac{\partial T}{\partial t}=\vec{\nabla}\cdot\left(\kappa T^{5/2}\,\vec{\nabla}T\right) $$ I know that, after discretization, the time step for the 1D ...
1
vote
2answers
1k views

How to handle floating point operations in HLSL?

I'm trying to write a perona malik anisotropic diffusion filter for the GPU. I'm basing my shader off a matlab implementation of the filter. I'm running into trouble because of what I suspect is ...
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 ...
5
votes
2answers
658 views

Are the drift-diffusion equations from semiconductor physics analogous to solving an advection-diffusion problem?

I am trying to understand an extra terms that appears when I derive the drift-diffusion equations for semiconductors. The extra term (see below) comes from applying the chain rule to the advection ...
6
votes
3answers
2k views

Open boundary conditions with the advection-diffusion equation

Following on from my previous equation I'm would like to apply open boundary condition to the advection-diffusion equation (with reaction term), $$ \frac{\partial \phi}{\partial t} = \frac{\partial}{\...
24
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)...
26
votes
2answers
4k 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 ...
7
votes
1answer
201 views

Optimal way to find stationary solutions of the PDE

I am researching heat diffusion in an optical element irradiated by laser. This problem is described by the PDE which I wrote down in this question. I am using an implicit numerical scheme to model ...
6
votes
1answer
161 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 ...