A flux solver based on discrete Boltzmann method for compressible flows with nonequilibrium effects

Abstract

A flux solver based upon the discrete Boltzmann method (DBM) is presented for simulating compressible flows that encompass both hydrodynamic and thermodynamic behaviors. The kinetic model utilizes discrete distribution functions expressed through the discrete equilibrium distribution function that is calculated via the inverse matrix method. Unlike the DBM using discrete Boltzmann equations, our approach solves the conservation equations of mass, momentum, and energy by calculating flux terms from the summation of discrete distribution functions. This method significantly enhances computational efficiency and numerical robustness compared to DBM, by employing fewer governing equations and allowing for larger time steps. The approach is validated through five standard benchmarks: sound wave, thermal Couette flow, Sod shock tube, Lax shock tube, and Kelvin–Helmholtz instability. Two discrete velocity sets at the Euler and Navier–Stokes levels are employed in the simulations. It is demonstrated that the flux solver effectively integrates the strengths of both hydrodynamic solvers and the DBM, offering a powerful tool for simulating and analyzing compressible flows with complex nonequilibrium features in diverse scientific and engineering applications.