Simulating Low-Mach Compressible Flow at Large Prandtl Numbers with a High-Order Fully-Implicit All-Speed Flow Solver

We present a high-order, fully-implicit fluid dynamics solver for simulating very low-Mach compressible flow. The work is motivated by the development of large-scale simulations of high-explosive cookoff, which requires modeling multi-species/multi-phase reactive flow at high Peclet numbers.

The governing equations are discretized in space up to 5^th-order 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, with the Jacobian-free version of the GMRES solver. We implement the low-Mach version of the AUSM+-up Riemann solver, which correctly mimics the pressure fluctuations of an incompressible flow solver in the asymptotic limit of small Mach number.

We demonstrate that our fully-implicit flow solver is able to robustly converge compressible flow calculations with Mach numbers less than 1.e-5. Furthermore, thin thermal boundary layers at high Prandtl numbers are easily resolved with a high-order discretization scheme.