Reaction-Diffusion - numerical simulation

[xcubic]

Hi to all,

I've been around this forum for some time now, but this is the first time I actually registered in need to ask you for some help to crack this. I've seen some great minds who surely could give me some lights. Thanks to all :)

Homework Statement

So, um trying to create a numerical simulation of a reaction-diffusion system (see eq. below) and I already did the numerical treatment and ok.
My goal is to build this on 2D and I already did on 1D and it went well.

Homework Equations

Here is my system of coupled equations:
du/dt = laplacian(u) + gamma * f(u,v)
dv/dt = d * laplacian(v) + gamma * g(u,v)

The Attempt at a Solution

I already build the simulation but it's not working as it should be. I want to know if someone already did try is hand at this and how it went? Maybe you could show me where to find some resources or show me some code/numerical recipes to me so I could make my simulation run properly.

Thanks to all, and sorry for my English, I'm not a natural English speaker and never really had English classes.

 

[KataKoniK]

Hello there,

It's great to see that you are working on a numerical simulation of a reaction-diffusion system. This is a very interesting and challenging problem that has many applications in various fields of science.

First of all, I would suggest checking your numerical treatment and making sure that it is correct. Sometimes, even small errors in the numerical treatment can lead to incorrect results. You can also try to simplify your system of equations and test it on a simpler case to make sure that your code is working properly.

In terms of resources, there are many books and articles on numerical methods for reaction-diffusion systems. One book that I would recommend is "Numerical Methods for Reaction-Diffusion Problems" by John Thoo. It covers various numerical methods for solving these types of systems and also provides code examples.

Additionally, you can also look for open-source codes or code repositories online that have already implemented numerical simulations of reaction-diffusion systems. This can give you a reference point and help you troubleshoot any issues in your own code.

I hope this helps and good luck with your simulation! Don't hesitate to ask for more specific help if needed.

 

[piercas]

Hello,

Reaction-diffusion systems are a fascinating field of study and numerical simulations are an important tool for understanding and predicting their behavior. It's great that you have already successfully created a 1D simulation and are now attempting to extend it to 2D.

One possible reason why your 2D simulation is not working as expected could be due to the differences in the numerical treatment between 1D and 2D. In 2D, the Laplacian operator is defined as the sum of the second derivatives in both x and y directions, while in 1D it is simply the second derivative in the x direction. This could lead to differences in the stability and accuracy of your simulation.

I would recommend checking your numerical treatment and making sure it is appropriate for a 2D system. You could also try looking for resources or code examples specifically for 2D reaction-diffusion simulations. Additionally, it would be helpful to compare your results with analytical solutions or experimental data to ensure the accuracy of your simulation.

Overall, keep experimenting and don't be discouraged if your simulation doesn't work perfectly at first. With some adjustments and fine-tuning, you will be able to create a successful 2D reaction-diffusion simulation.

Best of luck!