Assessment of a compressible lattice Boltzmann method in analyzing shock wave/boundary layer interaction in a supersonic inlet

The double distribution function lattice Boltzmann method (DDF LBM) has been explored for its potential applications in a supersonic inlet. The goal is to evaluate its ability to estimate the physics of shock wave/boundary layer interaction (SWBLI), including shock formation and separation bubble size. To validate the stability characteristics of DDF LBM, authors studied a well-known benchmark problem—the shock tube and the compressible flow around an airfoil. This involved calculating the propagation of normal and oblique shocks and predicting the location of contact discontinuities. Subsequently, the method was tested to predict the physics of shock wave and boundary layer interaction near a supersonic inlet. Notably, accurate predictions require careful consideration of space discretization, proper selection of the Courant-Friedrichs-Lewy (CFL) number, and parameter adjustments. Two discretization schemes—the fifth-order weighted essentially non-oscillatory (WENO) and the third-order weighted non-free-parameter dissipation (WNND) schemes—were assessed for their effectiveness in capturing the relevant physics.