Minimal number of discrete velocities for a flow description and internal structural evolution of a shock wave

TL;DR

This paper investigates the minimal set of discrete velocities needed to accurately model compressible thermal flows, using simulations to analyze shock wave internal structures with 25 or 33 velocities.

Contribution

It introduces a discrete velocity set for fluid flow modeling that achieves Navier-Stokes level accuracy with fewer velocities, optimizing computational efficiency.

Findings

Accurate shock wave simulations with 25 or 33 velocities.

Demonstrates internal structural evolution of shock waves.

Validates the minimal velocity set for thermal flow modeling.

Abstract

A fluid flow is described by fictitious particles hopping on homogeneously distributed nodes with a given finite set of discrete velocities. We emphasize that the existence of a fictitious particle having a discrete velocity among the set in a node is given by a probability. We describe a compressible thermal flow of the level of accuracy of the Navier-Stokes equation by 25 or 33 discrete velocities for two-dimensional space and perform simulations for investigating internal structural evolution of a shock wave.