I have recently learned about Discontinuous Galerkin method to solve differential equations and I was trying to implement it to solve Euler equation. For now, consider the standard Sod Shock Tube Case.
Without using any limiter I am getting an unstable scheme (even with CFL 0.01) and my solution blows up. Presently I am using 1st order polynomials in each cell using Lobatto nodes (in case someone needs to know). Also, I am calculating the interface flux using AUSM method.
Now I am not sure whether my code is wrong or does it behave like this because I haven't used any flux limiter?