A divergence-free-condition compensated method for incompressible Navier–Stokes equations

✍ Scribed by Tony W.H. Sheu; P.H. Chiu

• Book ID: 104013459
• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 961 KB
• Volume: 196
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/j.cma.2007.05.015

✦ Synopsis

The present study aims to develop a new formulation to effectively calculate the incompressible Navier-Stokes solutions in non-staggered grids. The distinguished feature of the proposed method, which avoids directly solving the divergence-free equation, is to add a rigorously derived source term to the momentum equation to ensure satisfaction of the fluid incompressibility. For the sake of numerical accuracy, dispersion-relation-preserving upwind scheme developed within the two-dimensional context was employed to approximate the convection terms. The validity of the proposed mass-preserving Navier-Stokes method is justified by solving two benchmark problems at high Reynolds and Rayleigh numbers. Based on the simulated Navier-Stokes solutions, the proposed formulation is shown to outperform the conventional segregated method in terms of the reduction of CPU time.