A Multi-Dimensional Shock-Capturing Limiter for High-Order Least Square-Based Finite Difference-Finite Volume Method on Unstructured Grids

A Multi-Dimensional Shock-Capturing Limiter for High-Order Least Square-Based Finite Difference-Finite Volume Method on Unstructured Grids

Year:    2021

Author:    Yangyang Liu, Liming Yang, Chang Shu, Huangwei Zhang

Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 3 : pp. 671–700

Abstract

In this paper, a simple and robust multi-dimensional shock-capturing limiter is presented and applied to the high-order least square-based finite difference-finite volume (LSFD-FV) method for simulation of compressible inviscid flows on unstructured grids. The novel limiter considers all the spatial information of the neighbouring supporting cells of the reference cell instead of only the immediate neighbours. As a result, the local upper and lower bounds can be correctly defined based on the extrema at specific points within the supporting stencil and thereafter the numerical oscillations in the adjacent region to the discontinuities can be suppressed effectively. The main advantage of this limiting technique lies in its simple methodology and easy implementation. Furthermore, the multi-dimensional character and the point extrema-based methodology endow the proposed limiter with ability to solve multi-dimensional flow problems on unstructured grids. A series of smooth and non-smooth numerical examples in one, two and three dimensions on unstructured grids are tested. Numerical results obtained demonstrate the superior performance of the proposed limiter on simulating compressible inviscid flows.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2020-0255

Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 3 : pp. 671–700

Published online:    2021-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    30

Keywords:    Shock-capturing limiter high-order finite volume method least square-based finite difference unstructured grids compressible inviscid flows.

Author Details

Yangyang Liu

Liming Yang

Chang Shu

Huangwei Zhang

  1. An efficient high-order least square-based finite difference-finite volume method for solution of compressible Navier-Stokes equations on unstructured grids

    Liu, Y.Y.

    Shu, C.

    Zhang, H.W.

    Yang, L.M.

    Lee, Cunbiao

    Computers & Fluids, Vol. 222 (2021), Iss. P.104926

    https://doi.org/10.1016/j.compfluid.2021.104926 [Citations: 8]