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.