## A unified finite element formulation for compressible and incompressible flows using augmented conservation variables.(English)Zbl 0943.76050

Summary: We propose a unified approach to computing compressible and incompressible flows. The governing equation for pressure is 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 compressible flows. We employ stabilized finite element formulations, based on the space-time and semi-discrete methods, with the ‘augmented’ conservation variables. 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.

### MSC:

 76M10 Finite element methods applied to problems in fluid mechanics 76N15 Gas dynamics (general theory) 76D05 Navier-Stokes equations for incompressible viscous fluids
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### References:

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