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

Authors

  • Bin Yu School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China.
  • Linying Li School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China.
  • Bin Zhang School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China.
  • Jianhang Wang School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China.

DOI:

https://doi.org/10.4208/cicp.OA-2015-0008

Keywords:

Detonation, spurious behavior, reactive Euler equations, threshold values method, stiffness.

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 multi-species and multi-reaction detonation test cases with strong stiffness are examined to illustrate the performance of the TVM approach.

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Published

2019-10-31

Issue

Vol. 22 No. 1 (2017)

Section

Articles