Simulating Multi-Species Compressible Reactive Flow at Low-Mach Number with a High-Order Fully-Implicit All-Speed Flow Solver

We present a high-order, fully-implicit all-speed fluid dynamics solver for simulating multi-species compressible reactive flow at very low-Mach numbers. The work is motivated by the development of high-explosive cookoff simulations, which requires modeling multi-species/multi-phase reactive melt convection physics over long time-scales. The governing equations are discretized in space up to 5$^{\mathrm{th}}$-order accuracy with a reconstructed Discontinuous Galerkin method and integrated in time with $L$-stable fully implicit time discretization schemes. The resulting set of non-linear equations is converged using a robust physics-block based preconditioned Newton-Krylov solver. We demonstrate that our fully-implicit flow solver is able to robustly converge multi-species compressible flow calculations with Mach numbers less than 10$^{\mathrm{-5}}$. Furthermore, our fully-implicit framework allows for large time steps relative to fast chemical kinetic timescales, which result in highly stiff linear systems.