Volume 22, Issue 1
An Approach to Obtain the Correct Shock Speed for Euler Equations with Stiff Detonation

Bin Yu, Linying Li, Bin Zhang & Jianhang Wang

Commun. Comput. Phys., 22 (2017), pp. 259-284.

Published online: 2019-10

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

  • Keywords

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

  • AMS Subject Headings

35Q31, 76L05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

zhangbin1983@sjtu.edu.cn (Bin Zhang)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-22-259, author = {Yu , Bin and Li , Linying and Zhang , Bin and Wang , Jianhang }, title = {An Approach to Obtain the Correct Shock Speed for Euler Equations with Stiff Detonation}, journal = {Communications in Computational Physics}, year = {2019}, volume = {22}, number = {1}, pages = {259--284}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/ 10.4208/cicp.OA-2015-0008}, url = {http://global-sci.org/intro/article_detail/cicp/13355.html} }
TY - JOUR T1 - An Approach to Obtain the Correct Shock Speed for Euler Equations with Stiff Detonation AU - Yu , Bin AU - Li , Linying AU - Zhang , Bin AU - Wang , Jianhang JO - Communications in Computational Physics VL - 1 SP - 259 EP - 284 PY - 2019 DA - 2019/10 SN - 22 DO - http://dor.org/ 10.4208/cicp.OA-2015-0008 UR - https://global-sci.org/intro/article_detail/cicp/13355.html KW - Detonation, spurious behavior, reactive Euler equations, threshold values method, stiffness. AB -

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.

Bin Yu, Linying Li, Bin Zhang & Jianhang Wang. (2019). An Approach to Obtain the Correct Shock Speed for Euler Equations with Stiff Detonation. Communications in Computational Physics. 22 (1). 259-284. doi: 10.4208/cicp.OA-2015-0008
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