On the Numerical Simulation of a Scramjet Intake using a Space-Time-Expansion Discontinuous Galerkin Scheme

Abstract

During the last years, discontinuous Galerkin (DG) methods became a prominent candidate for high order calculations since they combine high order spatial accuracy with geometrical exibility and further involve e ective parallelization. Hence, these features make the DG methods particularly suitable for complex large scale computations of a wide range of applications. A main drawback of high order schemes, though, is that they can lead to spurious oscillations when discontinuities, e.g. shock waves, are present within the ow eld. In order to prevent such non-physical oscillations, a shock capturing mechanism is required to robustly approximate the shocks. In this context, we will discuss an e cient arti cial viscosity based shock capturing mechanism within the Space-Time-Expansion discontinuous Galerkin (STE-DG) framework and apply it to typical shock capturing test cases and further to the three-dimensional simulation of the intake ow of a scramjet with a freestream Mach number of 8. As we focus on the shock waves and their proper resolution in a high order DG computation in this work, the numerical investigations base upon the inviscid Euler equations.