Upwind compact finite difference scheme for time-accurate solution of the incompressible Navier-Stokes equations
Upwind compact finite difference scheme for time-accurate solution of the incompressible Navier-Stokes equations
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DOI：
10.1016/j.amc.2009.10.001
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
A. Shah;Li Yuan;Aftab Khan
中科院分区：
文献类型：
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作者：
A. Shah;Li Yuan;Aftab Khan
本文提出了一种求解不可压Navier-Stokes方程的高精度紧致差分格式。该方法依赖于人工压缩性制定，这赋予控制方程的双曲抛物性质。对流项采用基于通量差分分裂的三阶迎风紧致格式离散，粘性项采用四阶中心紧致格式近似。采用双时间步结合Beam-Warming近似因式分解方法进行时间精确计算。通过对模型方程的分析和对四个标准流动问题的数值试验，将本紧致格式与已建立的非紧致格式进行了比较。结果表明，该三阶迎风紧致格式比非紧致格式具有更高的精度，而计算量与非紧致格式相当。
This article presents a time-accurate numerical method using high-order accurate compact finite difference scheme for the incompressible Navier–Stokes equations. The method relies on the artificial compressibility formulation, which endows the governing equations a hyperbolic–parabolic nature. The convective terms are discretized with a third-order upwind compact scheme based on flux-difference splitting, and the viscous terms are approximated with a fourth-order central compact scheme. Dual-time stepping is implemented for time-accurate calculation in conjunction with Beam-Warming approximate factorization scheme. The present compact scheme is compared with an established non-compact scheme via analysis in a model equation and numerical tests in four benchmark flow problems. Comparisons demonstrate that the present third-order upwind compact scheme is more accurate than the non-compact scheme while having the same computational cost as the latter.