Year: 2023
Author: Hao Zhang, Yidao Dong, Shichao Zheng, Xiaogang Deng
Communications in Computational Physics, Vol. 34 (2023), Iss. 2 : pp. 418–455
Abstract
In this paper, we present a hybrid form of weighted compact nonlinear scheme (WCNS) for hyperbolic conservation laws by applying linear and nonlinear methods for smooth and discontinuous zones individually. To fulfill this algorithm, it is inseparable from the recognition ability of the discontinuity detector adopted. In specific, a troubled-cell indicator is utilized to recognize unsmooth areas such as shock waves and contact discontinuities, while avoiding misjudgments of smooth structures. Some classical detectors are classified into three basic types: derivative combination, smoothness indicators and characteristic decomposition. Meanwhile, a new improved detector is proposed for comparison. Then they are analyzed through identifying a series of waveforms firstly. After that, hybrid schemes using such indicators, as well as different detection variables, are examined with Euler equations, so as to investigate their ability to distinguish practical discontinuities on various levels. Simulation results demonstrate that the proposed algorithm has similar performances to pure WCNS, while it generally saves 50 percent of CPU time for 1D cases and about 40 percent for 2D Euler equations. Current research is in the hope of providing some reference and establishing some standards for judging existing discontinuity detectors and developing novel ones.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2023-0080
Communications in Computational Physics, Vol. 34 (2023), Iss. 2 : pp. 418–455
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 38
Keywords: WCNS waveform detection troubled-cell indicator shock-capturing hybrid scheme.