High Order Numerical Simulation of Detonation Wave Propagation Through Complex Obstacles with the Inverse Lax-Wendroff Treatment (Communications in Computational Physics, 2020)
The high order inverse Lax-Wendroff (ILW) procedure is extended to boundarytreatment involving complex geometries on a Cartesian mesh. Our method ensuresthat the numerical resolution at the vicinity of the boundary and the inner domainkeeps the fifth order accuracy for the system of the reactive Euler equations with thetwo-step reaction model. Shock wave propagation in a tube with an array of rectangulargrooves is first numerically simulated by combining a fifth order weighted essentiallynon-oscillatory (WENO) scheme and the ILW boundary treatment. Comparedwith the experimental results, the ILW treatment accurately captures the evolution ofshock wave during the interactions of the shock waves with the complex obstacles.Excellent agreement between our numerical results and the experimental ones furtherdemonstrates the reliability and accuracy of the ILW treatment. Compared with theimmersed boundary method (IBM), it is clear that the influence on pressure peaks inthe 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 differentwidths of wall-mounted rectangular obstacles located on the lower wall. It isshown that the shock pressure along a horizontal line near the rectangular obstaclesgradually decreases, and the detonation cellular size becomes large and irregular withthe decrease of the obstacle width.