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Topic: Using PDE Toolbox to solve 2D advection equation
Replies: 5   Last Post: Feb 25, 2017 8:50 AM

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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$pcj$>...
> 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
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

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