Well-balanced discontinuous Galerkin method for Euler equations with gravity

We present a novel well-balanced discontinuous Galerkin scheme for compressible Euler equations with gravity and an ideal gas model. 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 well-balanced property is achieved by a specific form of source term discretization together with the GLL nodes. The scheme is able to preserve isothermal stationary solutions upto machine precision on any mesh composed of quadrilateral cells. It is applied on several examples using the numerical flux of Roe to demonstrate its well- balanced property and the improved resolution of small perturbations around the stationary solution.

People: Praveen C, Markus Zenk
Status: Completed, article accepted in Springer Journal of Scientific Computing