An efficient ψ‐v scheme for two‐dimensional laminar flow past bluff bodies on compact nonuniform grids,International Journal for Numerical Methods in Fluids

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An efficient ψ‐v scheme for two‐dimensional laminar flow past bluff bodies on compact nonuniform grids
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2020-04-19 , DOI: 10.1002/fld.4846
Pankaj Kumar ₁ , Jiten C. Kalita ₂

Affiliation

We recently proposed a second‐order accurate ψ‐v formulation of the steady‐state Navier‐Stokes (N‐S) equations on compact Cartesian nonuniform grids. In the current work, we extend the ideas of the aforesaid formulation and propose a second‐order spatially compact, implicit, stable ψ‐v formulation for the unsteady incompressible N‐S equations. Contrary to the existing ψ‐v finite difference formulations which use grid transformation, the proposed scheme is developed for nonuniform Cartesian grids without transformation specifically designed for two‐dimensional laminar flow past bluff bodies. It has been implemented on problems of internal flows inside curved regions as well as those involving fluid‐embedded body interaction. However, the robustness of the scheme is highlighted by the accurate resolution of a host of complex flows past bluff bodies with different physical set‐ups and boundary conditions. It was seen to handle problems involving both uniform and accelerated flows across a wide range of structures of varied shape, namely, a flat plate, a circular cylinder, inclined square cylinder, and a wedge in channel hinged to the wall. Apart from elegantly capturing all the details of the shedded vortex structures under different circumstances, the scheme was also able to handle both Dirichlet and Neumann boundary with equal ease. In all the cases, our results are found to be extremely close to the available numerical and experimental results.

中文翻译：

紧凑非均匀网格上二维流过钝体的有效ψ-v格式

我们最近提出了在紧凑的笛卡尔非均匀网格上的稳态Navier-Stokes（NS）方程的二阶精确ψ - v公式。在当前的工作中，我们扩展了上述公式的思想，并为非稳态不可压缩NS方程提出了二阶空间紧凑，隐式，稳定的ψ - v公式。与现有的ψ - v相反使用网格变换的有限差分公式，所提出的方案是为不均匀的笛卡尔网格而开发的，无需变换是专门为通过钝体的二维层流设计的。它已针对弯曲区域内部的内部流动问题以及涉及流体嵌入体相互作用的问题实施。但是，该方案的鲁棒性通过具有不同物理设置和边界条件的，经过钝体的大量复杂流的精确解析得到了强调。可以看到，它解决了涉及各种形状各异的结构的均匀流动和加速流动的问题，这些结构包括平板，圆柱体，倾斜的方形圆柱体以及铰接在墙上的楔形通道。除了优雅地捕获在不同情况下脱落的涡旋结构的所有细节外，该方案还能够同样轻松地处理Dirichlet和Neumann边界。在所有情况下，我们的结果都非常接近可用的数值和实验结果。

更新日期：2020-04-19

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