Volume 21, Issue 5
Designing Several Types of Oscillation-Less and High-Resolution Hybrid Schemes on Block-Structured Grids

Zhenhua Jiang, Chao Yan, Jian Yu & Boxi Lin

Commun. Comput. Phys., 21 (2017), pp. 1376-1407.

Published online: 2018-04

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  • Abstract

An idea of designing oscillation-less and high-resolution hybrid schemes is proposed and several types of hybrid schemes based on this idea are presented on block-structured grids. The general framework, for designing various types of hybrid schemes, is established using a Multi-dimensional Optimal Order Detection (MOOD) method proposed by Clain, Diot and Loub`ere [1]. The methodology utilizes low dissipation or dispersion but less robust schemes to update the solution and then implements robust and high resolution schemes to deal with problematic situations. A wide range of computational methods including central scheme, MUSCL scheme, linear upwind scheme and Weighted Essentially Non Oscillatory (WENO) scheme have been applied in the current hybrid schemes framework. Detailed numerical studies on classical test cases for the Euler system are performed, addressing the issues of the resolution and non-oscillatory property around the discontinuities.

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@Article{CiCP-21-1376, author = {Zhenhua Jiang, Chao Yan, Jian Yu and Boxi Lin}, title = {Designing Several Types of Oscillation-Less and High-Resolution Hybrid Schemes on Block-Structured Grids}, journal = {Communications in Computational Physics}, year = {2018}, volume = {21}, number = {5}, pages = {1376--1407}, abstract = {

An idea of designing oscillation-less and high-resolution hybrid schemes is proposed and several types of hybrid schemes based on this idea are presented on block-structured grids. The general framework, for designing various types of hybrid schemes, is established using a Multi-dimensional Optimal Order Detection (MOOD) method proposed by Clain, Diot and Loub`ere [1]. The methodology utilizes low dissipation or dispersion but less robust schemes to update the solution and then implements robust and high resolution schemes to deal with problematic situations. A wide range of computational methods including central scheme, MUSCL scheme, linear upwind scheme and Weighted Essentially Non Oscillatory (WENO) scheme have been applied in the current hybrid schemes framework. Detailed numerical studies on classical test cases for the Euler system are performed, addressing the issues of the resolution and non-oscillatory property around the discontinuities.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2015-0028}, url = {http://global-sci.org/intro/article_detail/cicp/11283.html} }
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