A Discontinuous Galerkin spectral-element method for high-speed reacting flows

A high-order discontinuous Galerkin spectral element method (DGSEM) is developed to solve the chemically reactive Euler equations. The numerical method, based on the spectral element solver Nek5000, includes detailed chemistry and thermodynamics to enable computations of chemically reactive flows, such as those encountered in high-speed combustion. To prevent aliasing errors associated with the high-order advection terms, the discontinuous Galerkin (DG) method employs a summation-by-parts (SBP) operator for the volumetric contribution, and the interface Riemann problem is treated with a local Lax-Friedrichs Flux (LFF). To handle flow discontinuities such as those encountered in shock waves, an entropy residual-based artificial viscosity is used. Unphysical oscillations are suppressed through a conservative positivity-preserving limiter. A validation study is first conducted for a one-dimensional H₂-O₂-Ar detonation, and the results are compared with the steady Zeldovich-von Neumann-Döring (ZND) solution. Following the successful code validation, an unsteady simulation of a two-dimensional detonation is performed with the same unburned mixture. Both qualitative and quantitative analyses are conducted to demonstrate the solver’s capability to adequately capture the detonation cellular structure as well as the temperature and species profiles throughout the detonation.