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首页> 外文期刊>Numerical Heat Transfer, Part B. Fundamentals: An International Journal of Computation and Methodology >ACCURATE DISCRETIZATION OF INCOMPRESSIBLE THREE-DIMENSIONAL NAVIER-STOKES EQUATIONS
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ACCURATE DISCRETIZATION OF INCOMPRESSIBLE THREE-DIMENSIONAL NAVIER-STOKES EQUATIONS

机译：不可压缩的三维Navier-Stokes方程的精确离散

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In this article an accurate discretization of three-dimensional incompressible Navier-Stokes equations is derived with the finite analytic method (FAM). The finite analytic method incorporates the local analytic solutions to formulate the discrete algebraic representations of partial differential equations. A very accurate 27-point finite analytic discretization scheme can be derived fron local analytic solutions of linearized three-dimensional convection-diffusion equations. Also, a computationally efficient 19-point finite analytic discretization scheme is derived utilizing the superposition of the local analytic solutions of linearized two-dimensional convection-diffusion equations. The accuracy of finite analytic discretization is analyzed. It is shown that using the 27-point scheme as an accurate benchmark case, the 19-point finite analytic numerical solution is computationally efficient and accurately simulates both convection and diffusion. Tn this study it is also shown that, due to the analytic nature of the solution, the finite analytic method provides an automatic, smooth, gradual upwinding of the three-dimensional convective effect. The finite analytic solutions are then obtained for the lid-driven cavity flow. The results are compared with previous computational results and available experiments. Good agreement is obtained. [References: 23]
机译：在本文中，使用有限解析方法（FAM）导出了三维不可压缩Navier-Stokes方程的精确离散化。有限解析方法结合了局部解析解，以表示偏微分方程的离散代数表示。可以从线性化三维对流扩散方程的局部解析解导出非常精确的27点有限解析离散方案。此外，利用线性化的二维对流扩散方程的局部解析解的叠加，得出了一种计算有效的19点有限解析离散化方案。分析了有限解析离散化的准确性。结果表明，使用27点方案作为精确的基准案例，该19点有限解析数值解在计算上是有效的，并且可以精确地模拟对流和扩散。在这项研究中，还表明，由于解的分析性质，有限分析方法为三维对流效应提供了自动，平滑，渐进的迎风。然后获得盖子驱动的腔体流动的有限解析解。将结果与以前的计算结果和可用的实验进行比较。获得良好的协议。 [参考：23]

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