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August 3, 2006, 18:41 
diffusion on surface of a sphere

#1 
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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 TWOdimensional!
This can be done in terms of spherical harmonics, but what I really want to do is solve the FokkerPlanck (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! 

August 4, 2006, 15:14 
Re: diffusion on surface of a sphere

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I have a Matlab code using divergencefree 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?


August 4, 2006, 15:52 
Re: diffusion on surface of a sphere

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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 2manifold. 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 FokkerPlanck 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 FokkerPlanck 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? 

August 4, 2006, 16:24 
Re: diffusion on surface of a sphere

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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 2D Finite Volume method on a moving surface in 3D (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, postprocessing etc is not as slick as the rest of OpenFOAM. For examples of this in action, have a look at the 3D 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 

August 9, 2006, 20:02 
Re: diffusion on surface of a sphere

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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 postprocessing 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 

August 22, 2006, 08:03 
Divergencefree finite element code

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Dear Jonas, I am now working a project for the stabilization of the NavierStiokes equation. I need to solve the linearized NavierStokes equation by using the divergencefree 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


August 22, 2006, 08:07 
Re: diffusion on surface of a sphere

#7 
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thanks


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