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Topic: Using PDE Toolbox to solve 2D advection equation
Replies: 3   Last Post: Mar 13, 2013 11:56 AM

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Torsten

Posts: 1,472
Registered: 11/8/10
Re: Using PDE Toolbox to solve 2D advection equation
Posted: Mar 13, 2013 9:18 AM
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"Nanna" wrote in message <khplse$pcj$1@newscl01ah.mathworks.com>...
> Hi all,
> I've been looking into the PDE Toolbox for teaching purposes. I've trawled through the Matlab Newsgroup but haven't been able to find a clear answer to this:
> I'm trying to find a simple way to use the toolbox to solve the advection equation in 2D:
> dT/dt=u*dT/dx+v*dT/dy
> where u and v are the (x,y)-components of a velocity field. There is no diffusion in the system so it's a first order problem. I have my own solution using finite differences, but I would really like to use the PDE Toolbox for comparison because of the finite element approach. All the examples I have found have been second order PDEs - does any one have a suggestion how to proceed? Preferably in a way that is suitable for demonstration to 2nd year physics students.
> Best,
> Nanna


AFAIK, there is no MATLAB tool to solve this kind of PDE.

Use CLAWPACK available under
http://depts.washington.edu/clawpack/
It is especially designed to solve hyperbolic PDEs in one, two and three space dimensions.

Or, if u and v are constant and the boundary conditions are simple,
it might even be possible to get an analytic solution for your problem above.

Best wishes
Torsten.



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