Multiple Pressure Variable (MPV) Approach for Low Mach Number Flows Based on Asymptotic Analysis

An asymptotic analysis of the compressible Euler equations in the limit of vanishing Mach numbers is used as a guideline for the development of a low Mach number extension of an explicit higher order shock capturing scheme. For moderate and large Mach numbers the underlying explicit compressible flow solver is active without modification. For low Mach numbers, the scheme employs an operator splitting technique motivated by the asymptotic analysis. Advection of mass and momentum as well as long wave acoustics are discretized explicitly, while in solving the sonic terms, the scheme uses an implicit pressure correction formulation to guarantee both divergence-free flow in the zero Mach number limit and appropriate representation of weakly nonlinear acoustic effects for small but finite Mach numbers. This asymptotics based approach is also used to show how to modify incompressible flow solvers to capture weakly compressible flows.

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