A Discontinuous Galerkin Spectral Element Method for Chemically Reacting Flows

This paper discusses the development of a discontinuous Galerkin spectral element method (DG-SEM) for multi-component hypersonic reacting flows. It specifically presents the method and its implementation in one dimension. A novel feature of this work is artificial dissipation applied to the characteristic variables. This more accurately scales the dissipation applied to contact discontinuities and allows for separate dissipation of each characteristic family. The artificial dissipation is activated with a new sensor design that can be cheaply calculated using only the local stencil, and can detect all types of discontinuities in a parameter-independent manner. Strang operator splitting is used to implicitly solve the chemical source terms separately from the convective and viscous terms. A wide variety of one-dimensional test cases are shown to validate the scheme.