Questions tagged [diffusion]

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Numerical solution to N-dimensional diffusion on simplex?

Assume I have a system of at least (but generally only) $N+1$ points in an $N$-dimensional space ($N > 3$ is possible). At each of these points $x_i, i=1,...,N+1$ I know an initial potential/...
3
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0answers
108 views

How to account for the interface between two different phases in a discretized diffusion model?

I have tried to set up a model for the diffusion of a gas into a liquid. The two media are next to each other and the geometry is spherical because the system should simulate the diffusion out of a ...
3
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0answers
196 views

Spurious oscillations in diffusion-reaction problems with finite volume

I have successfully solved the multi-species diffusion-reaction equation \begin{equation} \frac{\partial c_i}{\partial t} = \nabla \cdot (d_i(x)\nabla c_i) + s_i(x,t), \quad \quad (1) \end{equation} ...
2
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0answers
48 views

Modelling of Stefan Maxwell equation

I am trying to solve Maxwell Stefan's equation over a membrane to get the transient mole fraction distribution over the membrane thickness 'z'. But somehow I am not able to code it using ODE45, more ...
2
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0answers
76 views

Harmonic average of Diffusion Tensors in Finite Volume Method

I want to implement a Bilinear Finite Volume discretisation of the anisotropic diffusion problem: $$\frac{du}{dt} = \nabla \cdot (\textbf{D} \nabla u)$$ Both my degrees of freedom as well as the ...
2
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0answers
233 views

1 D Diffusion equation FDM with different layers

I'm trying to solve this particular equation $\frac{\partial u}{\partial t} = \frac{\partial}{\partial x} \big[D_{i}(x)\frac{\partial u}{\partial x} \big] + S(x,t)$ where the $i$ index denotes ...
1
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0answers
42 views

How to achieve (approx) unit scaling of a non-linear diffusion (heat) equation with a wildly varying diffusion coefficient?

I have numerical issues with a poorly scaled one-dimensional non-linear diffusion equation in physical co-ordinates $$ \frac{\partial{u}}{\partial{t}}(x,t) = \frac{\partial}{\partial{x}}\left(D(u) \...
1
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0answers
44 views

Unsteady diffusion equation with spatial finite elements and Forward Euler in time

I have solved the unsteady diffusion equation using piece-wise linear Finite elements(triangles) for spatial discretisation and Forward Euler for temporal discretisation. I have the following mesh ...
1
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0answers
63 views

Solving diffusion equation using finite difference method

I am solving an 1-dimensional diffusion equation with Neumann boundary condition at outlet and constant concentration, C, at the inlet. In the end, I want to observe how the concentration diffuses ...
1
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0answers
33 views

Setting up diffusion with integral B.C. in Fenics

I'm trying to model diffusion through a cylindrical domain $D = \{ (x,y,z) : x^2 + y^2 \leq 1, \;\; 0 \leq z \leq 1\}$. The is an initial concentration of the diffusant at the upper flat surface, ...
1
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0answers
41 views

Limit to volume change in a discretized mathematical model?

I have set up a mathematical model describing the diffusion of ozone out of a gas bubble. The bubble is surrounded by a thin gas film. So actually, the model describes the diffusion of ozone through ...
1
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0answers
184 views

Neumann boundary condition FD implementation for instationnary diffusion equation

I am trying to solve this diffusion equation : $\dfrac{\partial D\dfrac{\partial f}{\partial x}}{\partial x}+S = \dfrac{\partial f}{\partial t}$ ($D$ is not constant and varies according to $x$) with ...
1
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0answers
48 views

How is the Gastner-Newman equation implemented to create value-by-area cartograms?

There is a paper called "Density-equalizing map projections: Diffusion-based algorithm and applications" by Michael T. Gastner and M. E. J. Newman, which explains their algorithm (which is based in ...
1
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0answers
57 views

elliptic equation with exponential coefficient

I'm trying to solve the following equation $$\dfrac{\partial}{\partial x}\left(e^{au}\dfrac{\partial u}{\partial x}\right) = 0$$ Of course, this equation can be solved analytically. I am trying to ...
1
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0answers
226 views

Reaction-diffusion equations

I'm simulating a biological phenomena with reaction diffusion equations. There are multiple diffusing materials and there are some complex relations about consumption and production of such materials. ...
1
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0answers
144 views

Discontinuity at Interface

The equation at the left of the interface is \begin{equation} \displaystyle\frac{\partial C_i}{\partial t} = D_i \nabla^2 C_i - z_i \frac{D_i}{RT}F \nabla \cdot (C_i \nabla \phi_2) \end{equation} ...
1
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0answers
113 views

Reducing oscillations a 3D Alternating direction explicit scheme for the diffusion equation?

Hi I have made a 3D alternating direction explicit scheme for solving the diffusion equation, which will eventually replace a FTCS scheme in model of bubble dynamics in tissue. I have been testing it ...
0
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43 views

2D diffusion equation using Finite Volume Method

i am working on an assignment problem: Consider a two-dimensional rectangular plate of dimension L = 1 m in the x direction and H = 2 m in the y direction. The plate material has constant thermal ...
0
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0answers
69 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 ...
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24 views

Splitting coupled non-linear diffusion equations into blocks

Two coupled linear diffusion equations $$\begin{split}\partial_ta&=\nabla(\nabla a)\\ \partial_tb&=\nabla(\nabla b)\end{split}$$ can be split into blocks by putting everything onto one side, ...
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312 views

3D Diffusion Equation in Fourier space

I'm solving the 3D Diffusion equation $$u_t=k(u_{xx}+u_{yy}+u_{zz})$$ in MATLAB using Fourier techniques. I assume a 3D Fourier expansion $(e^{-ipx},e^{-imy},e^{-imz})$of the solution. Physical ...
0
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0answers
215 views

advection diffusion equation

Would you know what is the condition for stability for the advection-diffusion equation where we treat the diffusion part using Crank-Nicholson and the advection part using FCTS (forward in time ...