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High Order Well-Balanced Weighted Compact Nonlinear Schemes for the Gas Dynamic Equations under Gravitational Fields

Part of: Hyperbolic equations and systems

Published online by Cambridge University Press:  31 January 2018

Zhen Gao  and
Guanghui Hu
Zhen Gao*
Affiliation:
School of Mathematical Sciences, Ocean University of China, Qingdao, China
Guanghui Hu*
Affiliation:
Department of Mathematics, University of Macau, Macao SAR, China UM Zhuhai Research Institute, Zhuhai, Guangdong Province, China
*
*Corresponding author. Email addresses:zhengao@ouc.edu.cn (Z. Gao), garyhu@umac.mo (G. H. Hu)
*Corresponding author. Email addresses:zhengao@ouc.edu.cn (Z. Gao), garyhu@umac.mo (G. H. Hu)
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Abstract

In this study, we propose a high order well-balanced weighted compact nonlinear (WCN) scheme for the gas dynamic equations under gravitational fields. The proposed scheme is an extension of the high order WCN schemes developed in (S. Zhang, S. Jiang, C.-W Shu, J. Comput. Phys. 227 (2008) 7294-7321). For the purpose of maintaining the exact steady state solution, the well-balanced technique in (Y. Xing, C.-W Shu, J. Sci. Comput. 54 (2013) 645-662) is employed to split the source term into two terms. The proposed scheme can maintain the isothermal equilibrium solution exactly, genuine high order accuracy and resolve small perturbations of the hydrostatic balance state on the coarse meshes. Furthermore, in order to capture the strong discontinuities and large gradients, the fifth-order upwind weighted nonlinear interpolations together with the fourth/sixth order cell-centered compact schemes with local characteristic projections are used to construct different WCN schemes. Several representative one- and two-dimensional examples are simulated to demonstrate the good performance of the proposed schemes.

Keywords

Euler equationsgravitational fieldssource termsteady state solutionweighted compact nonlinear Scheme

MSC classification

Secondary: 35L65: Conservation laws 35L67: Shocks and singularities
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 7 , Issue 4 , November 2017 , pp. 697 - 713
Copyright
Copyright © Global-Science Press 2017 

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