A Boltzmann scheme with physically relevant discrete velocities for Euler equations

TL;DR

This paper introduces a new discrete velocity Boltzmann scheme aligned with physical wave speeds for solving Euler equations, offering a simpler alternative to traditional kinetic methods.

Contribution

It presents a novel approach to selecting discrete velocities based on physical wave speeds, improving the applicability of Boltzmann schemes to gas dynamics.

Findings

Scheme effectively solves Euler equations

Discrete velocities correspond to physical wave speeds

Simplifies kinetic scheme implementation

Abstract

Kinetic or Boltzmann schemes are interesting alternatives to the macroscopic numerical methods for solving the hyperbolic conservation laws of gas dynamics. They utilize the particle-based description instead of the wave propagation models. While the continuous particle velocity based upwind schemes were developed in the earlier decades, the discrete velocity Boltzmann schemes introduced in the last decade are found to be simpler and are easier to handle. In this work, we introduce a novel way of introducing discrete velocities which correspond to the physical wave speeds and formulate a discrete velocity Boltzmann scheme for solving Euler equations.