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Designing Several Types of Oscillation-Less and High-Resolution Hybrid Schemes on Block-Structured Grids

Part of: Computer aspects of numerical algorithms Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  27 March 2017

Zhenhua Jiang ,
Chao Yan ,
Jian Yu  and
Boxi Lin
Zhenhua Jiang*
Affiliation:
College of Aeronautics Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, P.R. China
Chao Yan*
Affiliation:
College of Aeronautics Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, P.R. China
Jian Yu*
Affiliation:
College of Aeronautics Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, P.R. China
Boxi Lin*
Affiliation:
College of Aeronautics Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, P.R. China
*
*Corresponding author. Email addresses:zhenhua122122@163.com (Z. Jiang), yanchao@buaa.edu.cn (C. Yan), yuj@buaa.edu.cn (J. Yu), boxi_lin@163.com (B. Lin)
*Corresponding author. Email addresses:zhenhua122122@163.com (Z. Jiang), yanchao@buaa.edu.cn (C. Yan), yuj@buaa.edu.cn (J. Yu), boxi_lin@163.com (B. Lin)
*Corresponding author. Email addresses:zhenhua122122@163.com (Z. Jiang), yanchao@buaa.edu.cn (C. Yan), yuj@buaa.edu.cn (J. Yu), boxi_lin@163.com (B. Lin)
*Corresponding author. Email addresses:zhenhua122122@163.com (Z. Jiang), yanchao@buaa.edu.cn (C. Yan), yuj@buaa.edu.cn (J. Yu), boxi_lin@163.com (B. Lin)
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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 Loubère [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.

Keywords

Hybrid schemesoscillation-lesshigh resolutionMOODfinite volume

MSC classification

Secondary: 65Y20: Complexity and performance of numerical algorithms 65M08: Finite volume methods

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 5 , May 2017 , pp. 1376 - 1407
Copyright
Copyright © Global-Science Press 2017 

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