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High Order Numerical Simulation of Detonation Wave Propagation Through Complex Obstacles with the Inverse Lax-Wendroff Treatment

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Shock waves and blast waves

Published online by Cambridge University Press:  23 November 2015

Cheng Wang ,
Jianxu Ding ,
Sirui Tan  and
Wenhu Han
Cheng Wang*
Affiliation:
State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing, 100081, P.R. China
Jianxu Ding
Affiliation:
State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing, 100081, P.R. China
Sirui Tan
Affiliation:
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
Wenhu Han
Affiliation:
Center for Combustion Energy, Tsinghua University, Beijing, 100084, P.R. China
*
*Corresponding author. Email address:wangcheng@bit.edu.cn (C. Wang)
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Abstract

The high order inverse Lax-Wendroff (ILW) procedure is extended to boundary treatment involving complex geometries on a Cartesian mesh. Our method ensures that the numerical resolution at the vicinity of the boundary and the inner domain keeps the fifth order accuracy for the system of the reactive Euler equations with the two-step reaction model. Shock wave propagation in a tube with an array of rectangular grooves is first numerically simulated by combining a fifth order weighted essentially non-oscillatory (WENO) scheme and the ILW boundary treatment. Compared with the experimental results, the ILW treatment accurately captures the evolution of shock wave during the interactions of the shock waves with the complex obstacles. Excellent agreement between our numerical results and the experimental ones further demonstrates the reliability and accuracy of the ILW treatment. Compared with the immersed boundary method (IBM), it is clear that the influence on pressure peaks in the reflected zone is obviously bigger than that in the diffracted zone. Furthermore, we also simulate the propagation process of detonation wave in a tube with three different widths of wall-mounted rectangular obstacles located on the lower wall. It is shown that the shock pressure along a horizontal line near the rectangular obstacles gradually decreases, and the detonation cellular size become large and irregular with the decrease of the obstacle width.

Keywords

Boundary treatmentdetonationinverse Lax-Wendrofftwo-step reaction modelWENO scheme.

MSC classification

Secondary: 65M06: Finite difference methods 76L05: Shock waves and blast waves
Type
Research Article
Information
Communications in Computational Physics , Volume 18 , Issue 5 , November 2015 , pp. 1264 - 1281
Copyright
Copyright © Global-Science Press 2015 

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