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# A Staggered Grid Method for Solving Incompressible Flow on Unstructured Meshes

Huawen Shu, Minghai Xu, Xinyue Duan*, Yongtong Li, Yu Sun, Ruitian Li, Peng Ding
College of New Energy, China University of Petroleum (East China), Qingdao, 266580, China
* Corresponding Author: Xinyue Duan. Email:
(This article belongs to this Special Issue: Advances in Modeling and Simulation of Complex Heat Transfer and Fluid Flow)

Computer Modeling in Engineering & Sciences 2020, 123(2), 509-523. https://doi.org/10.32604/cmes.2020.08806

Received 11 October 2019; Accepted 03 January 2020; Issue published 01 May 2020

### Abstract

A finite volume method based unstructured grid is presented to solve the two dimensional viscous and incompressible flow. The method is based on the pressure-correction concept and solved by using a semi-staggered grid technique. The computational procedure can handle cells of arbitrary shapes, although solutions presented in this paper were only involved with triangular and quadrilateral cells. The pressure or pressure-correction value was stored on the vertex of cells. The mass conservation equation was discretized on the dual cells surrounding the vertex of primary cells, while the velocity components and other scale variables were saved on the central of primary cells. Since the semi-staggered arrangement can’t guarantee a strong coupling relationship between pressure and velocity, thus a weak coupling relationship leads to the oscillations for pressure and velocity. In order to eliminate such an oscillation, a special interpolation scheme was used to construct the pressure-correction equation. Computational results of several viscous flow problems show good agreement with the analytical or numerical results in previous literature. This semi-staggered grid method can be applied to arbitrary shape elements, while it has the most efficiency for triangular cells.

### Keywords

Staggered grid; incompressible flow; pressure correction; finite volume method

Shu, H., Xu, M., Duan, X., Li, Y., Sun, Y. et al. (2020). A Staggered Grid Method for Solving Incompressible Flow on Unstructured Meshes. CMES-Computer Modeling in Engineering & Sciences, 123(2), 509–523.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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