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

Abstract

To kinetically model implosion- and explosion-related phenomena, we present a theoretical framework for constructing a discrete Boltzmann model (DBM) with spherical symmetry in spherical coordinates. To achieve this goal, a key technique is to use localCartesian coordinates to describe the particle velocity in the kinetic model. Therefore, geometric effects, such as divergence and convergence, are described as a “force term”. To better access the nonequilibrium behavior, even though the corresponding hydrodynamic model is one-dimensional, the DBM uses a discrete velocity model (DVM) with three dimensions. A new scheme is introduced so that the DBM can use the same DVM regardless of whether or not there are extra degrees of freedom. As an example, a DVM with 26 velocities is formulated to construct the DBM at the Navier–Stokes level. Via the DBM, one can study simultaneously the hydrodynamic and thermodynamic nonequilibrium behaviors in implosion and explosion processes that are not very close to the spherical center. The extension of the current model to a multiple-relaxation-time version is straightforward.

Keywords

discrete Boltzmann model / compressible flows / spherical symmetry / geometric effects / thermodynamic nonequilibrium

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