TY - JOUR T1 - A Third-Order Upwind Compact Scheme on Curvilinear Meshes for the Incompressible Navier-Stokes Equations JO - Communications in Computational Physics VL - 2-4 SP - 712 EP - 729 PY - 2009 DA - 2009/02 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7759.html KW - AB -

This paper presents a new version of the upwind compact finite difference scheme for solving the incompressible Navier-Stokes equations in generalized curvilinear coordinates. The artificial compressibility approach is used, which transforms the elliptic-parabolic equations into the hyperbolic-parabolic ones so that flux difference splitting can be applied. The convective terms are approximated by a third-order upwind compact scheme implemented with flux difference splitting, and the viscous terms are approximated by a fourth-order central compact scheme. The solution algorithm used is the Beam-Warming approximate factorization scheme. Numerical solutions to benchmark problems of the steady plane Couette-Poiseuille flow, the lid-driven cavity flow, and the constricting channel flow with varying geometry are presented. The computed results are found in good agreement with established analytical and numerical results. The third-order accuracy of the scheme is verified on uniform rectangular meshes.