Simulation of multiple shock–shock interference using implicit anti‐diffusive WENO schemes

Abstract

SUMMARYAccurate computations of two-dimensional turbulent hypersonic shock-shock interactions that arise when single and dual shocks impinge on the bow shock in front of a cylinder are presented. The simulation methods used are a class of lower-upper symmetric-Gauss-Seidel implicit anti-diffusive weighted essentially non-oscillatory (WENO) schemes for solving the compressible Navier-Stokes equations with Spalart-Allmaras one-equation turbulence model. A numerical flux of WENO scheme with anti-diffusive flux correction is adopted, which consists of first-order and high-order fluxes and allows for a more flexible choice of first-order dissipative methods. Experimental flow fields of type IV shock-shock interactions with single and dual incident shocks by Wieting are computed. By using the WENO scheme with anti-diffusive flux corrections, the present solution indicates that good accuracy is maintained and contact discontinuities are sharpened markedly as compared with the original WENO schemes on the same meshes. Computed surface pressure distribution and heat transfer rate are also compared with experimental data and other computational results and good agreement is found.