On limiting for higher order discontinuous Galerkin method for 2D Euler equations
We present an implementation of discontinuous Galerkin method for 2-D Euler equations on Cartesian meshes using tensor product Lagrange polynomials based on Gauss nodes. The scheme is stabilized by a version of the slope limiter which is adapted for tensor product basis functions together with a positivity preserving limiter. We also incorporate and test shock indicators to determine which cells need limiting. Several numerical results are presented to demonstrate that the proposed approach is capable of computing complex discontinuous flows in a stable and accurate fashion.
Keywordspartial differential equations conservation laws discontinuous Galerkin method limiters compressible Euler equations shock indicator
Mathematical subject classification35L65