I use discontinuous galerkin method to solve steady flow 1D shallow water equations

  with the bump at the bottom and this flow is frictionless.

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

The solution that I have get always blow up and not correspond with the exact solution, I think that I maybe approximate source term incorrectly but I don't know how to fix this problem.

Could anyone suggest me?

thank you!!

ps. I am Thai and not good in English.

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?