Discrete Boltzmann modeling of unsteady reactive flows with nonequilibrium effects

Abstract

A multiple-relaxation-time discrete Boltzmann model (DBM) is proposed for multicomponent mixtures, where compressible, hydrodynamic, and thermodynamic nonequilibrium effects are taken into account. It allows the specific heat ratio and the Prandtl number to be adjustable, and is suitable for both low and high speed fluid flows. From the physical side, besides being consistent with the multicomponent Navier-Stokes equations, Fick's law and Stefan-Maxwell diffusion equation in the hydrodynamic limit, the DBM provides more kinetic information about the nonequilibrium effects. The physical capability of DBM to describe the nonequilibrium flows, beyond the Navier-Stokes representation, enables the study of the entropy production mechanism in complex flows, especially in multicomponent mixtures. Moreover, the current kinetic model is employed to investigate the compressible nonequilibrium Kelvin-Helmholtz instability (KHI). It is found that, in the dynamic KHI process, the mixing degree and fluid flow are similar for cases with various thermal conductivity and initial temperature configurations. Physically, both heat conduction and temperature exert slight influences on the formation and evolution of the KHI.

Hydrodynamic and Thermodynamic Nonequilibrium Effects around Shock Waves: Based on a Discrete Boltzmann Method

“…It is noteworthy that the DBM has the capability of measuring the nonequilibrium manifestations in subsonic, sonic and supersonic flows accurately [29][30][31][32][33][34][35][36][37][38][39]. Actually, the DBM is capable to recover the velocity distribution function in two ways.…”

“…The other type of kinetic models is to capture both hydrodynamic and thermodynamic nonequilibrium behaviours beyond the macroscopic models. The successful physical models include the unified gas kinetic scheme [24][25][26], the discrete unified gas kinetic scheme [27,28], the discrete Boltzmann method (DBM) [29][30][31][32][33][34][35][36][37][38][39], etc. These powerful models are suitable for continuum and rarefied systems with a wide range of Knudsen numbers, and capable to subsonic and supersonic flows with essential nonequilibrium effects.…”

“…From a physical modeling perspective, a DBM is approximately equivalent to a continuous fluid model plus a coarse-grained model of other relevant thermodynamic nonequilibrium effects. At present, the DBM has been developed as a nonequilibrium flow simulation tool for various flow systems, including the fluid instability [29,32,38], multiphase flow [34], shock and detonation [30,31,33,36,37,39]. Roughly speaking, the DBMs can be classed into two categories: the single-relaxation-time DBM [29][30][31][32][33][34][35][36] and the multiple-relaxation-time DBM [37][38][39].…”

“…In this article, we use the multiple-relaxation-time DBM to study nonequilibrium shock waves, where both specific heat ratio and Prandtl number are adjustable [39]. Thanks to its kinetic nature, the versatile DBM can be adopted to capture and measure both hydrodynamic and thermodynamic nonequilibrium behaviours in an accurate and effective way [39]. The DBM is briefly introduced in Appendix A.…”

Lattice–Gas–Automaton Modeling of Income Distribution

“…The microdynamics of such an artificial world should be as simple as possible for the sake of high computational efficiency [ 31 , 36 ]. Furthermore, the LGA was the precursor to the lattice Boltzmann method (LBM) [ 36 , 37 , 38 , 39 , 40 , 41 ] and discrete Boltzmann method (DBM) [ 42 , 43 , 44 , 45 , 46 , 47 , 48 ]. In a broad sense, the LGA and its offspring (LBM/DBM) are regarded as mesoscopic kinetic models with the following similar virtues.…”