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?

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    $\begingroup$ Hi, Thida! It would be nice if you provide some more details for those who are not familiar with this problem. $\endgroup$ – faleichik Feb 6 '12 at 18:54
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    $\begingroup$ It would be helpful to see your integral equation, and the discretization of your source term. $\endgroup$ – Paul Feb 6 '12 at 20:11
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    $\begingroup$ 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. $\endgroup$ – Allan P. Engsig-Karup Feb 6 '12 at 20:41
  • $\begingroup$ Have you looked at Frank Giraldo's work? He does a lot of DG work for shallow water. $\endgroup$ – Jeremy Kozdon Feb 7 '12 at 5:53
  • $\begingroup$ scicomp.stackexchange.com/questions/59/… seems to be a similar question as this one. You might find your answer in there. $\endgroup$ – Subodh Apr 21 '13 at 18:29