Three-Dimensional Lattice Boltzmann Model for High-Speed Compressible Flows

A highly efficient three-dimensional (3D) Lattice Boltzmann (LB) model for high-speed compressible Sowsis proposed.This model is developed from the original one by Kataoka and Tsutahara [Phys.Rev.E 69 (2004) 056702].The convection term is discretized by the Non-oscillatory, containing No free parameters and Dissipative (NND) scheme,which effectively damps oscillations at discontinuities.To be more consistent with the kinetic theory of viscosity and tofurther improve the numerical stability, an additional dissipation term is introduced.Model parameters are chosen insuch a way that the von Neumann stability criterion is satisfied.The new model is validated by well-known benchmarks,(i) Riemann problems, including the problem with Lax shock tube and a newly designed shock tube problem with highMach number; (ii) reaction of shock wave on droplet or bubble.Good agreements are obtained between LB results andexact ones or previously reported solutions.The model is capable of simulating flows from subsonic to supersonic andcapturing jumps resulted from shock waves.