A One-Dimensional Discrete Boltzmann Method for Multidimensional Compressible Flows

Abstract

A simple and efficient one-dimensional discrete Boltzmann method is developed for compressible flows with tunable specific heat ratios by incorporating extra degrees of freedom. To guarantee Galilean invariance in numerical simulations, a discrete velocity set is constructed with high spatial symmetry. Furthermore, an operator-splitting scheme is proposed to extend the one-dimensional kinetic formulation to simulations of one-, two-, and three-dimensional flow systems within a unified framework. The proposed model and numerical method are verified and validated against several benchmark problems, including the Sod shock tube, Lax shock tube, 2D Riemann problem, uniform translational flow, and acoustic wave propagation. The results demonstrate the accuracy, robustness, and flexibility of the present approach for compressible flow simulations.