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



Torsten
Posts:
1,717
Registered:
11/8/10


Re: Using PDE Toolbox to solve 2D advection equation
Posted:
Mar 13, 2013 9:18 AM


"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.



