A cross-dimensional discrete Boltzmann framework for fluid dynamics

TL;DR

This paper introduces a versatile discrete Boltzmann method for simulating compressible fluid flows across multiple dimensions, emphasizing accuracy, robustness, and computational efficiency.

Contribution

It presents a novel one-dimensional discrete Boltzmann framework with tunable heat ratios, high symmetry velocity sets, and an operator-splitting scheme for multi-dimensional flows.

Findings

Accurately simulates shock tube and acoustic wave problems.

Demonstrates robustness across various benchmark tests.

Flexible for one-, two-, and three-dimensional flow simulations.

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, uniform translational flow, and acoustic wave propagation. The results demonstrate the accuracy, robustness, and flexibility of the present approach for compressible flow simulations.