Discrete Boltzmann model for implosion and explosion related compressible flow with spherical symmetry

TL;DR

This paper develops a Discrete Boltzmann Model with spherical symmetry to simulate implosion and explosion phenomena, capturing both hydrodynamic and thermodynamic nonequilibrium behaviors in spherical flows.

Contribution

It introduces a novel DBM framework using local Cartesian coordinates and a unified DVM scheme for spherical symmetry, enabling detailed kinetic analysis of implosion and explosion processes.

Findings

Successfully models nonequilibrium behaviors in spherical implosion/explosion

Uses a 26-velocity DVM for Navier-Stokes level simulations

Framework adaptable to multiple relaxation times

Abstract

To kinetically model implosion and explosion related phenomena, we present a theoretical framework for constructing Discrete Boltzmann Model(DBM) with spherical symmetry in spherical coordinates. To this aim, a key technique is to use \emph{local} Cartesian coordinates to describe the particle velocity in the kinetic model. Thus, the geometric effects, like the divergence and convergence, are described as a \textquotedblleft force term\textquotedblright. To better access the nonequilibrium behavior, even though the corresponding hydrodynamic model is one-dimensional, the DBM uses a Discrete Velocity Model(DVM) with 3 dimensions. A new scheme is introduced so that the DBM can use the same DVM no matter considering the extra degree of freedom or not. As an example, a DVM with 26 velocities is formulated to construct the DBM in the Navier-Stokes level. Via the DBM, one can study simultaneously the hydrodynamic and thermodynamic nonequilibrium behaviors in the implosion and explosion process which are not very close to the spherical center. The extension of current model to the multiple-relaxation-time version is straightforward.