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Runge-Kutta Discontinuous Galerkin Method with Front Tracking Method for Solving the Compressible Two-Medium Flow on Unstructured Meshes

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Hyperbolic equations and systems

Published online by Cambridge University Press:  11 October 2016

Haitian Lu ,
Jun Zhu ,
Chunwu Wang  and
Ning Zhao
Haitian Lu*
Affiliation:
College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 210016, China
Jun Zhu*
Affiliation:
College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 210016, China
Chunwu Wang*
Affiliation:
College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 210016, China
Ning Zhao*
Affiliation:
College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 210016, China
*
*Corresponding author. Email:lhtgkzy@126.com (H. T. Lu), zhujun@nuaa.edu.cn (J. Zhu), wangcw@nuaa.edu.cn (C. W. Wang), nzhao2000@hotmail.com (N. Zhao)
*Corresponding author. Email:lhtgkzy@126.com (H. T. Lu), zhujun@nuaa.edu.cn (J. Zhu), wangcw@nuaa.edu.cn (C. W. Wang), nzhao2000@hotmail.com (N. Zhao)
*Corresponding author. Email:lhtgkzy@126.com (H. T. Lu), zhujun@nuaa.edu.cn (J. Zhu), wangcw@nuaa.edu.cn (C. W. Wang), nzhao2000@hotmail.com (N. Zhao)
*Corresponding author. Email:lhtgkzy@126.com (H. T. Lu), zhujun@nuaa.edu.cn (J. Zhu), wangcw@nuaa.edu.cn (C. W. Wang), nzhao2000@hotmail.com (N. Zhao)
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Abstract

In this paper, we extend using the Runge-Kutta discontinuous Galerkin method together with the front tracking method to simulate the compressible two-medium flow on unstructured meshes. A Riemann problem is constructed in the normal direction in the material interfacial region, with the goal of obtaining a compact, robust and efficient procedure to track the explicit sharp interface precisely. Extensive numerical tests including the gas-gas and gas-liquid flows are provided to show the proposed methodologies possess the capability of enhancing the resolutions nearby the discontinuities inside of the single medium flow and the interfacial vicinities of the two-medium flow in many occasions.

Keywords

Runge-Kutta discontinuous Galerkin methodfront tracking methodtwo-medium flowRiemann problemunstructured mesh

MSC classification

Secondary: 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 65M99: None of the above, but in this section 35L65: Conservation laws
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 1 , February 2017 , pp. 73 - 91
Copyright
Copyright © Global-Science Press 2017 

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