What is the difference between a free boundary problem and a moving boundary problem?
What methods are applicable to each kind? And where is the starting point in learning the numerical methods for a free boundary problem like flooding?
Main difference:
Moving boundary - boundary motion is prescribed.
Free boundary - boundary motion is result of calculation.
Free boundary problems are more complicated, because of interaction of fluid and it's surface and is similar to interaction of fluid and structure (FSI).
The FEM explicite ALE approach can be used (ABAQUS, LS-DYNA).
Probably the mesh-free method are applicable as well.
I have just started studying the shallow water equations. I have solved and implemented the Riemann Problem for the 1-D case. I now want to implement a finite volume scheme for the same 1-D SWEs but the result I get seem totally different from the exact solution. I evaluated numerical fluxes F at boundary interfaces using F(U_) where U_ is the variable value at boundary cells and evaluated inter-cell fluxes using F(Ustar) where Ustar is a solution of the Riemann Problem with initial data from the average values of U in the bounding cells.
What could be the cause of the disparity?
I could paste the exact functions here, if you don't mind.
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