Low-diffusion flux-splitting methods for flows at all speeds

Methods for extending the advective upwind splitting method (AUSM) family of low-diffusion flux-splitting schemes to operate effectively at all how speeds are developed. The extensions developed are designed for use with time-derivative preconditioning and are based on the idea that the speed of sound should cease to be an important scaling parameter for the diffusive contributions to the interface flux as the Mach number becomes small. Using this criterion, alternative definitions for the interface Mach numbers are developed, and methods for ensuring pressure-velocity coupling at low speeds are formulated. Results are presented for inviscid flows through a channel at various Mach numbers, developing viscous flow in a two-dimensional duct, driven-cavity Bows at various Mach and Reynolds numbers, flow over a backward-facing step, and hydrogen-nitrogen mixing lagers.