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首页> 外文期刊>Journal of Computational Physics >A 6th order staggered compact finite difference method for the incompressible Navier-Stokes and scalar transport equations
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A 6th order staggered compact finite difference method for the incompressible Navier-Stokes and scalar transport equations

机译：不可压缩的Navier-Stokes和标量输运方程的6阶交错紧凑有限差分方法

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摘要

In a previous paper we have developed a staggered compact finite difference method for the compressible Navier-Stokes equations. In this paper we will extend this method to the case of incompressible Navier-Stokes equations. In an incompressible flow conservation of mass is ensured by the well known pressure correction method [7,21]. The advection and diffusion terms are discretized with 6th order spatial accuracy. The discrete Poisson equation, which has to be solved in the pressure correction step, has the same spatial accuracy as the advection and diffusion operators. The equations are integrated in time with a third order Adams-Bashforth method. Results are presented for a 1D advection-diffusion equation, a 2D lid driven cavity at a Reynolds number of 1000 and 10,000 and finally a 3D fully developed turbulent duct flow at a bulk Reynolds number of 5400. In all cases the methods show excellent agreement with analytical and other numerical and experimental work.
机译：在以前的论文中，我们为可压缩的Navier-Stokes方程开发了交错的紧凑有限差分方法。在本文中，我们将把这种方法扩展到不可压缩的Navier-Stokes方程的情况。在不可压缩的流动中，通过众所周知的压力校正方法可确保质量守恒[7,21]。对流和扩散项以六阶空间精度离散化。必须在压力校正步骤中求解的离散泊松方程具有与对流和扩散算子相同的空间精度。方程通过三阶Adams-Bashforth方法及时积分。给出了一维对流扩散方程，雷诺数分别为1000和10,000的2D盖驱动腔以及最后雷诺数为5400的3D完全展开的湍流导管流动的结果。在所有情况下，这些方法均与分析和其他数值和实验工作。

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