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

High-speed gaseous combustion plays a critical role in both propulsion and power generation applications such as scramjets and detonation engines. These systems involve disparate spatio-temporal scales due to the interaction of turbulence, chemistry and compressibility, and necessitate both accurate and efficient numerical algorithms. With recent advances in computational hardware, high-order numerical methods have gained traction in the high-speed combustion community due to their strong balance between accuracy and computational cost. In this talk, I’ll focus specifically on the development of a novel discontinuous Galerkin spectral element method (DGSEM) for the chemically reacting Navier-Stokes equations. To handle the disparate length and time scales associated with these equations, the numerical method combines the spectral accuracy of the SEM with the flexibility of the DG approach. An entropy-residual based artificial viscosity is added to smooth shocked regions of flow, and a positivity-preserving limiter is implemented to suppress non-physical oscillations. A series of smooth and discontinuous validation cases are presented in increasing physical and computational complexity for both inviscid and viscous flows. In particular, simulations of canonical two-dimensional detonations are performed, and the high-order numerical results are validated against experimental and numerical data. Additional validation studies are carried out for classical three-dimensional numerical simulations of incompressible and compressible turbulent flows.