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An Approach to Obtain the Correct Shock Speed for Euler Equations with Stiff Detonation

Part of: Shock waves and blast waves Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  03 May 2017

Bin Yu ,
Linying Li ,
Bin Zhang  and
Jianhang Wang
Bin Yu
Affiliation:
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China
Linying Li
Affiliation:
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China
Bin Zhang*
Affiliation:
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China
Jianhang Wang
Affiliation:
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China
*
*Corresponding author. Email address:zhangbin1983@sjtu.edu.cn (B. Zhang)
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Abstract

Incorrect propagation speed of discontinuities may occur by straightforward application of standard dissipative schemes for problems that contain stiff source terms for underresolved grids even for time steps within the CFL condition. By examining the dissipative discretized counterpart of the Euler equations for a detonation problem that consists of a single reaction, detailed analysis on the spurious wave pattern is presented employing the fractional step method, which utilizes the Strang splitting. With the help of physical arguments, a threshold values method (TVM), which can be extended to more complicated stiff problems, is developed to eliminate the wrong shock speed phenomena. Several single reaction detonations as well as multispecies and multi-reaction detonation test cases with strong stiffness are examined to illustrate the performance of the TVM approach.

Keywords

Detonationspurious behaviorreactive Euler equationsthreshold values methodstiffness

MSC classification

Secondary: 35Q31: Euler equations 76L05: Shock waves and blast waves
Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 1 , July 2017 , pp. 259 - 284
Copyright
Copyright © Global-Science Press 2017 

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Footnotes

Communicated by Chi-Wang Shu

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