A unified finite element formulation for compressible and incompressible flows using augmented conservation variables

Abstract

A unified approach to computing compressible and incompressible flows is proposed. The governing equation for pressure is selected based on the local Mach number. In the incompressible limit the divergence-free constraint on velocity field determines the pressure, while it is the equation of state that governs the pressure solution for the compressible flows. Stabilized finite element formulations, based on the space-time and semi-discrete methods, with the 'augmented' conservation variables are employed. The 'augmented' conservation variables consist of the usual conservation variables and pressure as an additional variable. The formulation is applied to various test problems involving steady and unsteady flows over a large range of Mach and Reynolds numbers.