A new finite element formulation for both compressible and nearly incompressible fluid dynamics
A new finite element formulation designed for both compressible and nearly incompressible viscous flows is presented. The formulation combines conservative and non-conservative dependent variables, namely, the mass-velocity (density*velocity), internal energy and pressure. The central feature of the method is the derivation of a discretized equation for pressure, where pressure contributions arising from the mass, momentum and energy balances are taken implicitly in the time discretization. The method is applied to the analysis of laminar flows governed by the Navier-Stokes equations in both compressible and nearly incompressible regimes. Numerical examples, covering a wide range of Mach number, demonstrate the robustness and versatility of the new method. Copyright (C) 2000 John Wiley & Sons, Ltd.
finite element formulation mass-velocity compressible flow nearly incompressible flow