# Questions tagged [diffusion]

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45 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 ...
35 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, ...
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 ...
200 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 ...
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 ...
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 ...
228 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. ...
315 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 ...
153 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} ...
114 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 ...
54 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 ...
198 views

### Numerically solving a non-linear PDE

I have this non-linear partial differential equation. $$\frac{\partial C}{\partial t}=\left(\frac{\partial C}{\partial x}\right)^2+C\frac{\partial^2 C}{\partial x^2}$$ I want to use the finite ...
279 views

### Numerical Solution of non-linear diffusion equation using Finite Differencing

I'm trying to solve the following non-linear diffusion equation: $$\frac{\partial}{\partial t} u(x,t)= \frac{\partial^{2}}{\partial x^{2}}u(x,t)^{3}$$ $$-1\leq x \leq1, t \geq 0$$ with the boundary ...
390 views

### Stable implicit method to solve convection-heat diffusion in 3D

The last couple of hours I have been looking for an unconditionally stable method to solve the convection-diffusion equation within a 3D inhomogeneous material. Here's the well known diffusion-...
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 ...
84 views

### Stability of PDEs

I am currently trying to solve some PDEs with FiPy. At page 56, the manual mentions (https://www.ctcms.nist.gov/fipy/download/fipy-3.0.pdf). The largest stable timestep that can be taken for this ...
74 views

### Simulating Brownian motion in 3-D for first hitting time?

I want to simulate Brownian motion in 3-D for the following conditions: $$p(x=0,y=0,z=0,t=0)=1$$ $$p(x,y,z=c,t)=0$$ where $p$ is the probability of finding molecules in the 3-D environment. I want to ...
42 views

### Solving the diffusion/heat equation for a randomly distributed set of points in 3D

In this problem I am trying to solve, I have a messy set of points distributed in 3D space, each with a defined temperature. If I would want to calculate the heat transfer scenario in this system, how ...