Well-balanced discontinuous Galerkin method for Euler equations with gravity
We discuss a well-balanced discontinuous Galerkin scheme for compressible Euler equations with gravity. The DG scheme is based on nodal discontinuous Lagrange basis functions supported at Gauss-Lobatto-Legendre (GLL) nodes together with GLL quadrature using the same nodes. The scheme is able to preserve isothermal and polytropic stationary solutions upto machine precision on any mesh composed of quadrilateral cells. We provide numerical examples to show the performance of the scheme.