A Positivity Preserving Discontinuous Galerkin Method for Hypersonic Flow of Thermally Perfect Gases

A discontinuous Galerkin method is developed for a multi-species system of PDEs involving the thermally perfect gas equation of state. A conservative projection of limited quantities (CPL) is used in order to reduce the oscillations occurring due to closure-law inconsistencies in high-order simulations. Several hypersonic simulations are presented to verify the correct implementation of the equation of state and limiter. The CPL method stabilizes computations which would otherwise fail due to negative temperatures. However, noticeable oscillations in temperature are still present in cases where the shock is misaligned with the grid, requiring further investigation.