# Questions tagged [diffusion]

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### 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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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}{\...
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)...
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 ...