High order discontinuous Galerkin discretizations with a new limiting approach and positivity preservation for strong moving shocks

Abstract

Accurate predictions of skin friction and thermal loads of high speed complex flows in both simple and nontrivial geometries, require high resolution computations. High order discontinuous Galerkin (DG) discretizations possess features that make them very attractive for computation of complex flows with strong shocks. The key ingredient that would make the DG method suitable for these computations, is application of p-adaptive procedures that ensure accurate capturing of discontinuities with low order approximations and resolution of smooth complex features, such as vortices and shear layers, with higher order accuracy. A limiting procedure of DG discretizations capable of computing high speed flows with strong shocks around complex geometries using a p-adaptive procedure on mixed type meshes is used and positivity is enforced on pressure and density for flows with large expansions. The unified slope limiting combined with the positivity limiters are applied for a number of inviscid flows with strong shocks to demonstrate the potential of the method.