Questions tagged [diffusion]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
1
vote
1answer
300 views

Unfolding folded trajectories for Diffusivity calculation - MD

I have just started using dl_poly classic to work in Molecular Dynamics simulations. It produces a HISTORY file which records the trajectory after applying boundary conditions. Now, here I don't ...
2
votes
1answer
156 views

Problem with Richardson extrapolation method for weak convergence in SDE

I have implemented the Richardson extrapolation of the Euler-Maruyama method to 4th order, to estimate the moments of SDE. The Euler-Maruyama works, and I would expect the Richardson extrapolation to ...
0
votes
0answers
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 ...
4
votes
2answers
683 views

Diffusion coefficient when simulating in 2D

Suppose I want to simulate the well-known diffusion partial differential equation in 2D, for example with finite elements or finite differences. Can I directly take physical diffusion coefficients ...
1
vote
0answers
146 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} ...
6
votes
2answers
2k views

9-point stencil finite difference Laplacian with variable diffusion coefficients

So I'm trying to implement a 9-point stencil discretization to the 2D difussion equation. The stencil is here. However, most of the literature deals with a Laplacian that has a constant diffusion ...
1
vote
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 ...
2
votes
2answers
798 views

Determining if samples fit a 3D Gaussian distribution

I have a collection of sample particles, with (x,y,z) coordinates generated by a simplified Monte Carlo-like code. I expect that these particles will follow an anisotropic diffusion process, which ...
2
votes
1answer
181 views

Not getting correct numerical solution for Advection-Diffusion-Reaction eqn

Objective: I am trying to numerically solve $C(x,y,t)$ from the following advection-diffusion-reaction equation in 2D space (x,y) and time. I will be testing my numerical solution with an approximate ...
2
votes
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
vote
1answer
77 views

Reaction-Diffusion problem A->B, solving for B

I need to solve a Reaction-Diffusion using Finite Elements, piecewise linear elements. In this problem, a reaction $A \rightarrow B$, with rate law $ r_A = - k_A \cdot u_A $, takes part, where $u_i$ ...
2
votes
2answers
271 views

Model of heat sink problem with fan

I am trying to solve this problem using advection-diffusion model and finite element method for the solution, due to the complex geometry. Basically the problem i'm trying to solve using OpenFOAM is ...
2
votes
1answer
145 views

Modified diffusion equation and unstabilities

I am trying to simulate the phase separation of a binary mixture. If the free energy F is known as a function of the concentration $c$, the dynamical equation is: $ \frac{\partial c(x,t)}{\partial t}=...
0
votes
1answer
265 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 ...
4
votes
1answer
535 views

Two approaches to solving diffusion equation in Fourier space

I want to numerically solve the diffusion equation $\partial_t u = D \partial_x^2 u$ in Fourier space, and can think of multiple ways to do it. Setup Option 1 Differentiating $u$ twice in Fourier ...
2
votes
2answers
356 views

Computing element stiffness matrices with variable coefficients

I am trying to implement a simple FEM approach, using p1 triangular elements, for solving the diffusion equation with variable nodal diffusivities and I was wondering how to incorporate the variable ...
0
votes
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 ...
3
votes
1answer
227 views

High frequency noise at solving diffusion equation

I'm trying to simulate a simple diffusion based on Fick's 2nd law. ...
4
votes
1answer
232 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
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 ...
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 ...
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 ...
1
vote
2answers
2k 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 ...
5
votes
2answers
744 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
3k 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}{\...
7
votes
1answer
219 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
168 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 ...

1
2