Discontinuous Galerkin Method for Compressible Viscous Reacting Flow

In the present study, a discontinuous Galerkin (DG) framework is developed to simulate chemically reacting flows. The algorithm combines a double-flux method to account for variable thermodynamic properties, a Strang-splitting scheme for the stiff reaction chemistry, a robust WENO-based shock limiter, and the non-linear viscous-diffusive transport is discretized using the BR2 method. The algorithm is verified and validated by considering a series of oneand two-dimensional test cases, and results are compared with self-similarity solutions and experiments to examine critical algorithmic components. These cases include low-Mach deflagration systems and supersonic inviscid and viscous problems. Multi-dimensional configurations consider the shock-flame interaction and detonation initiation process. It is shown that the reactive DG-method provides an accurate description of key-physical mechanisms that control the ignition onset in confined detonation systems.