Computational study of shock-wave interaction with solid obstacles using immersed boundary methods

In this study, an immersed boundary (IB) method based on a direct forcing is coupled with a high-order weighted-essentially non-oscillatory (WENO) scheme to simulate fluid-solid interaction (FSI) problems with complex geometries. The IB is a general simulation method for FSI, whereas the WENO is an efficient scheme for fluid flow simulations and shock waves, and both of them work on regular cartesian grids. The effectiveness and the accuracy of the coupled scheme are first analyzed on well-documented supersonic test problems for a wide range of Mach numbers. The results are in good agreement with both analytical and experimental data. A comprehensive analysis of the interaction of the moving shock through an array of cylinder matrix is then conducted by varying the number of cylinders in the matrix block while keeping the same opening passage. The relaxation length between two adjacent columns of cylinders is kept identical to study uniquely the effect of surface-to-volume ratio of the obstacle matrix. It is shown that the configuration with higher surface-to-volume ratio produces more post-shock flow instabilities downstream of the matrix block. The complex shock/shock and shock/vortex interactions are well resolved by the present computation. It is being observed that after the passage of the shock through the cylinder matrix, eddies of different length scales are generated, but the later stage of shock/vortex and shocklet/vortexlet interactions are different for the two cases. The analysis of the PSD of the total kinetic energy globally conforms to Richardson's inviscid cascade. An intermittent peaked PDF of downstream instantaneous vorticity field is obtained in the limit of Re→∞. The baroclinic production of vorticity is found to be feeble as previously founded by Sun and Takayama (J. Fluid Mech. 2003; 478:237-256).