Development of Discontinuous Galerkin Method for Detonation and Supersonic Combustion

A discontinuous Galerkin algorithm for the simulation of realistic detonation and supersonic combustion systems is developed. This algorithm enables to consider complex and temperature/mixture-dependent thermodynamic transport properties, detailed and stiff reaction chemistry, and the robust shock-capturing. In order to evaluate all relevant algorithmic aspects, the DG-method is applied to a series of test-cases of increasing physical complexity: Begin with binary thermal advection and multi-species shock-tube problems, the accuracy and conservation properties of the double-flux formulation and the shockcapturing scheme are investigated. Following this analysis, simulations of a multi-species Argon-diluted Hydrogen/Oxygen detonation system are conducted using a detailed chemical kinetics mechanism. By considering refinement in polynomial order, mesh-refinement, and comparisons with second-order FV-solution, it is shown that optimal convergence rates are achieve and that polynomial refinement provides advantages in better resolving the Zeldovich-Neumann-Döring (ZND) flame structure behind the shock.