High order discontinuous Galerkin simulation of hypersonic shock-boundary layer interaction using subcell limiting approach

Abstract

Numerical simulation of shock-boundary layer interactions in the hypersonic regime has for long been a challenge, plagued by high sensitivity of the surface predictions to grid and numerical details. In the course of developing adaptive high order methods to mitigate this issue, discontinuous Galerkin method has emerged as a promising alternative to the conventionally used finite volume method. However, till date, among the reported finite element method-based simulations of these flows, only a few have presented high order simulations using a higher than linear basis. In this work, a subcell limiting technique devised for the compressible Navier-Stokes equations is extended for use in the hypersonic regime. The proposed extension is tested by performing simulations of several shock-boundary layer interaction cases in the freestream Mach number range 6 to 14 using a quadratic basis. For a set of cases at Mach 6, grid converged simulations are presented that agree reasonably well with experimental data and other numerical solutions. More importantly, simulations of a Mach 11 case that are performed using two different flux schemes are shown to yield nearly identical predictions of the surface pressure and heat transfer, suggesting that high order solutions can reduce the sensitivity of numerical predictions to the computational details. Grid convergence studies of two cases at Mach numbers 11 and 14 led to observing large scale oscillations in the separation bubble in finer grid simulations, suggesting that explicit time integration may not always be suitable for high order computation of hypersonic separated flows at very high Mach numbers.