Does anyone have simple code for this (e.g., MatLab), assuming there is no flux in nor out of the sphere, ie, it is only TWO-dimensional!

This can be done in terms of spherical harmonics, but what I really want to do is solve the Fokker-Planck (diffusion/convection) on the sphere, so I would rather 'modify' existing code for this.

Also, I intend to add stochastic terms to it; all the more reason I don't want to start from scratch!

Thanks in advance!

I have a Matlab code using divergence-free finite elements that I think would be almost trivial to modify for the surface of a sphere. I know what the spherical surface elements look like. What would a test problem look like?

Thank you very much, Jonas!

Indeed, my problem is simple: I just want to solve the diffusion equation on the surface (2D problem) of a sphere. There is no flux in nor out, i.e., it is a 2-manifold.

On a plane, the equation is u_t = u_xx + u_yy or

u_t = laplacian u

This has been worked on by many people (although I find the approach of spherical harmonics most intuitive), but what I ultimately want to do is solve Fokker-Planck on the surface of the sphere. This is just a diffusion/convection/reaction equation, so I will just add the other terms.

Then I would like to add small perturbations to the radius of the sphere, to simulate a cell that is growing.

The Fokker-Planck on this growing cell has theoretical results from Paris 6, and they need numerical work done on this.

This is where I come in. If you have the code for simple diffusion on the unit sphere, and are willing to share it, that would be great. Do you have a paper I can cite?

Hi,

Well, I've got an option for you, but it's not trivial. A student of mine did a series of simulations of free rising bubbles of air in water with mesh deformation and surfactant effects in OpenFOAM. In order to handle the surfactant behaviour, he/we implemented a 2-D Finite Volume method on a moving surface in 3-D (I call it Finite Area).

The code is freely available and shipped as a part of OpenFOAM - I can also give you some examples + there is a series of comparisons in the PhD Thesis.

The reason I say this is not trivial is that mesh generation, post-processing etc is not as slick as the rest of OpenFOAM. For examples of this in action, have a look at the 3-D rising bubble simulations in some of my slides, e.g.

http://www.h.jasak.dial.pipex.com/pr...t_7Apr2005.pdf

on page 23.

Hrv

Thank you very much, Hrv!

Just snooped around your presentation, and indeed, your application is not trivial, but might very well be the proper approach to one application I have in mind, viz, a growing cell (start with a sphere, and randomly perturb the radius in space and time). I know people who have theoretical results for this.

It does not matter that the post-processing is not 'slick', right now, I am in the 'study' phase, so that is the least of my problems.

Will appreciate links to downloads, and examples you can provide.

Thank you very much for taking the time.

Pearl

Dear Jonas, I am now working a project for the stabilization of the Navier-Stiokes equation. I need to solve the linearized Navier-Stokes equation by using the divergence-free finite element space. Could you please share your matlab code? Thank you very much. This is the first time I found this message place. I am very appreciated that you could write to my email address Y.Yan@sheffield.ac.uk for some information of the code. Best regards, Yubin Yan

thanks