PHYSICALLY CORRECT PENALTY-LIKE FORMULATIONS FOR ACCURATE PRESSURE CALCULATION IN FINITE-ELEMENT ALGORITHMS OF THE NAVIER-STOKES EQUATIONS

Finite element algorithms for incompressible fluids, in particular the penalty function method, are re-examined and re-formulated based on p hysically consistent approximations to the mass conservation equation. These approximations lead to methods that satisfy all fluid condition s under the assumption of slightly compressible flow and directly yiel d approximations to the pressure field that are free from spurious osc illations. Penalty function-type algorithms are developed for direct s teady-state calculations and for time-dependent simulations of viscous incompressible flows that are based on the bilinear isoparametric qua drilateral element and circumvent the Ladyszhenskaya, Babuska and Brez zi (LBB) condition. Furthermore, methods that eliminate pressure oscil lations in the low Mach number region of high-speed compressible flows are obtained. These methods are tested in examples that show their su perior performance in approximating the pressure field.