Physically correct penalty-like formulations for accurate pressure calculation in finite element algorithms of the Navier-Stokes equations

✍ Scribed by B. R. Dyne; J. C. Heinrich

• Publisher: John Wiley and Sons
• Year: 1993
• Tongue: English
• Weight: 1017 KB
• Volume: 36
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620362208

✦ Synopsis

Abstract

Finite element algorithms for incompressible fluids, in particular the penalty function method, are re‐examined and re‐formulated based on physically consistent approximations to the mass conservation equation. These approximations lead to methods that satisfy all fluid conditions under the assumption of slightly compressible flow and directly yield approximations to the pressure field that are free from spurious oscillations. Penalty function‐type algorithms are developed for direct steady‐state calculations and for time‐dependent simulations of viscous incompressible flows that are based on the bilinear isoparametric quadrilateral element and circumvent the Ladyszhenskaya, Babuska and Brezzi (LBB) condition. Further‐more, methods that eliminate pressure oscillations in the low Mach number region of high‐speed compressible flows are obtained. These methods are tested in examples that show their superior performance in approximating the pressure field.