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I use the discontinuous galerkin method to solve the steady flow 1D shallow water equations with a bump at the bottom. This flow is frictionless.

I use the runge-kutta method to approximate the time derivative of these equations and gauss-lobatto quadrature to approximate the integral equation in the weak form of the source term.

The solution that I get always blows up and doesn't correspond with the exact solution, I think that I may be approximating the source term incorrectly but I don't know how to fix this problem.

Any suggestions?

Paul
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Thida
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    Hi, Thida! It would be nice if you provide some more details for those who are not familiar with this problem. – faleichik Feb 06 '12 at 18:54
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    It would be helpful to see your integral equation, and the discretization of your source term. – Paul Feb 06 '12 at 20:11
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    You need to detail your problem. What is the choice of numerical fluxes in the scheme? Also, is it sub- or super-critical flow? (important to understand whether shocks will develop). How is the bump defined? Have you tried testing against an analytical solution to this problem? How do you impose boundary conditions? etc. – Allan P. Engsig-Karup Feb 06 '12 at 20:41
  • Have you looked at Frank Giraldo's work? He does a lot of DG work for shallow water. – Jeremy Kozdon Feb 07 '12 at 05:53
  • http://scicomp.stackexchange.com/questions/59/how-to-construct-well-balanced-finite-volume-and-discontinuous-galerkin-methods seems to be a similar question as this one. You might find your answer in there. – Subodh Apr 21 '13 at 18:29
  • Given that this question is vague, and the OP hasn't visited the site in a long while, I'm going to close this question and consider it for deletion later. – Geoff Oxberry May 24 '13 at 05:11

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