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Upwind discretization schemes for the incompressible Navier-Stokes equations

机译：不可压缩的Navier-Stokes方程的Upwind分散化方案

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Two upwind schemes for solving the incompressible Navier-Stokes equations using the recently developed Helmholtz Decomposition method are presented. In one scheme vorticity is extrapolated from the walls to the centres of the momentum cells as a function of the sign of the velocity, while in the other scheme one of the derivatives in the expression for vorticity is evaluated via one-sided differences. Application of the schemes to flows over a backward facing step and a flat plate demonstrates that while both schemes are stable, vorticity extrapolation results in a more accurate vorticity field. Since upwinding is applied only to the rotational term of the momentum equations in Lamb form and artificial sources of vorticity are eliminated by the Helmholtz Decomposition method, the side-effects of upwinding are greatly reduced. A finite difference discretization on a staggered grid is used and a segregated solution procedure is employed.
机译：介绍了使用最近开发的Helmholtz分解方法求解不可压缩的Navier-Stokes方程的两个载入方案。在一种方案中，作为速度符号的函数，从壁从壁外推开从壁到动量细胞的中心，而在其他方案中，通过单边的差异评估涡度表达中的衍生物中的一种。这些方案在向后面对面流动的应用，平板显示出，虽然两个方案都是稳定的，但是涡旋外推导致更准确的涡旋场。由于覆盖器仅应用于羊肉形式的动量方程的旋转项，并且通过Helmholtz分解方法消除了人工源的旋转来源，因此覆盖的副作用大大降低。使用交错网格上的有限差异离散化，采用分离的解决方案程序。

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