Two-dimensional finite-difference lattice Boltzmann method for the complete Navier-Stokes equations of binary fluids

TL;DR

This paper introduces a two-dimensional finite-difference lattice Boltzmann method capable of simulating compressible, thermal binary fluid mixtures by relaxing previous constraints, validated through Couette flow and relaxation process tests.

Contribution

It develops a novel lattice Boltzmann method based on Sirovich's kinetic theory and a 61-velocity model, enabling simulation of complete Navier-Stokes equations for binary fluids.

Findings

Successfully simulates compressible and thermal binary fluids.

Validates method with Couette flow and relaxation process.

Releases previous constraints on isothermal and nearly incompressible systems.

Abstract

Based on Sirovich's two-fluid kinetic theory and a dodecagonal discrete velocity model, a two-dimensional 61-velocity finite-difference lattice Boltzmann method for the complete Navier-Stokes equations of binary fluids is formulated. Previous constraints, in most existing lattice Boltzmann methods, on the studied systems, like isothermal and nearly incompressible, are released within the present method. This method is designed to simulate compressible and thermal binary fluid mixtures. The validity of the proposed method is verified by investigating (i) the Couette flow and (ii) the uniform relaxation process of the two components.