PDE solver on 2D sphere

2018 8 29
1 个回答
更新时间：2018 9 4
3 次查看（30 天）

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Hi,
I would like to solve a spatio-temporal non-linear PDE on a 2D sphere (not a 'shell' with a finite thickness).
I see there is a number of mesh generators (cubed sphere, icosahedral grid) for Matlab, but how to integrate them with a PDE solver?
Is it possible with PDEtoolbox or other Matlab tools? Any examples?
Climate modelers probably do this all the time...

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Amal George M
Amal George M 2018-9-3
Hi Mark,
MATLAB Partial Differential Equations Toolbox support both 2D and 3D geometries. You can find a couple of examples at this link . Time dependency can also be integrated into the problem, by providing a list of time instances to the ' solvepde ' function.
Syntax:
result = solvepde(model,timelist);
Here is an example involving time-varying results.
Hope this helps.
Mark vanRossum
Mark vanRossum 2018-9-3
Thank you, but I would like to solve on a sphere, which is a 2D object embedded in 3D space.
I don't see how that fits in the PDEtoolbox which either requires 3D objects (which a sphere is not) or 2D objects embedded in 2D space.
The only solution I currently see is to make it a shell of finite thickness.
Torsten
Torsten 2018-9-3
You could calculate on a rectangle if you use spherical coordinates ...
Best wishes
Torsten.
Mark vanRossum
Mark vanRossum 2018-9-3
That's a good idea Torsten. Will the poles give trouble, and do I need special boundary conditions there?
Torsten
Torsten 2018-9-3
I don't know. My guess is that the periodic boundary condition will be the most difficult part to deal with when using the PDE toolbox.
Best wishes
Torsten.

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回答（1 个）

Ravi Kumar
Ravi Kumar 2018-9-4

0 个投票

If you are referring to thin walled hollow sphere, a 3-D volume as your problem domain, then you can create such geometry in PDE Toolbox as:
radius = 1;
thickness = radius/10;
gm = multisphere([radius-thickness, radius], 'Void',[1,0]);
model = createpde;
model.Geometry = gm;
pdegplot(model,'FaceLabels','on','FaceAlpha',0.3,'CellLabels','on')
print('Hollow_Sphere','-dpng','-r200')

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