Finite-Difference Lattice Boltzmann Methods for binary fluids

TL;DR

This paper develops finite-difference lattice Boltzmann methods based on two-fluid BGK kinetic models for binary fluids, capable of handling symmetric and asymmetric systems with different masses and temperatures.

Contribution

It introduces new kinetic models C, D, and E for asymmetric systems and combines them with finite-difference schemes to accurately simulate binary fluid dynamics.

Findings

Validated methods with uniform relaxation tests

Successfully simulated isothermal Couette flow

Accurately modeled diffusion behavior

Abstract

We investigate two-fluid BGK kinetic methods for binary fluids. The developed theory works for asymmetric as well as symmetric systems. For symmetric systems it recovers Sirovich's theory and is summarized in models A and B. For asymmetric systems it contributes models C, D and E which are especially useful when the total masses and/or local temperatures of the two components are greatly different. The kinetic models are discretized based on an octagonal discrete velocity model. The discrete-velocity kinetic models and the continuous ones are required to describe the same hydrodynamic equations. The combination of a discrete-velocity kinetic model and an appropriate finite-difference scheme composes a finite-difference lattice Boltzmann method. The validity of the formulated methods is verified by investigating (i) uniform relaxation processes, (ii) isothermal Couette flow, and (iii) diffusion behavior.