A discrete Boltzmann model with symmetric velocity discretization for compressible flow

Abstract

A discrete Boltzmann model (DBM) with symmetric velocity discretization is constructed for compressible systems with an adjustable specific heat ratio in the external force field. The proposed two-dimensional (2D) nine-velocity scheme has better spatial symmetry and numerical accuracy than the discretized velocity model in literature [Acta Aerodyn. Sin. 40 98108 (2022)] and owns higher computational efficiency than the one in literature [Phys. Rev. E 99 012142 (2019)]. In addition, the matrix inversion method is adopted to calculate the discrete equilibrium distribution function and force term, both of which satisfy nine independent kinetic moment relations. Moreover, the DBM could be used to study a few thermodynamic nonequilibrium effects beyond the Euler equations that are recovered from the kinetic model in the hydrodynamic limit via the Chapman–Enskog expansion. Finally, the present method is verified through typical numerical simulations, including the free-falling process, Sod’s shock tube, sound wave, compressible Rayleigh–Taylor instability, and translational motion of a 2D fluid system.