Two-fluid discrete Boltzmann model for compressible flows: based on Ellipsoidal Statistical Bhatnagar-Gross-Krook

TL;DR

This paper introduces a two-fluid Discrete Boltzmann Model based on ES-BGK for simulating compressible flows, allowing flexible thermodynamic properties and capturing non-equilibrium behaviors beyond traditional Navier-Stokes models.

Contribution

The paper develops a novel two-fluid DBM with adjustable Prandtl number and specific heat ratio, enabling detailed non-equilibrium analysis in compressible flows.

Findings

Model accurately reproduces benchmark test results.

Captures non-equilibrium phenomena not seen in traditional models.

Provides a flexible framework for binary fluid simulations.

Abstract

A two-fluid Discrete Boltzmann Model(DBM) for compressible flows based on Ellipsoidal Statistical Bhatnagar-Gross-Krook(ES-BGK) is presented. The model has flexible Prandtl number or specific heat ratio. Mathematically, the model is composed of two coupled Discrete Boltzmann Equations(DBE). Each DBE describes one component of the fluid. Physically, the model is equivalent to a macroscopic fluid model based on Navier-Stokes(NS) equations, and supplemented by a coarse-grained model for thermodynamic non-equilibrium behaviors. To obtain a flexible Prandtl number, a coefficient is introduced in the ellipsoidal statistical distribution function to control the viscosity. To obtain a flexible specific heat ratio, a parameter is introduced in the energy kinetic moments to control the extra degree of freedom. For binary mixture, the correspondence between the macroscopic fluid model and the DBM may be several-to-one. Five typical benchmark tests are used to verify and validate the model. Some interesting non-equilibrium results, which are not available in the NS model or the single-fluid DBM, are presented.