Hybrid lattice Boltzmann model for binary fluid mixtures

TL;DR

This paper introduces a hybrid lattice Boltzmann method for simulating binary fluid mixtures, improving stability and reducing spurious velocities through a free-energy approach and refined discretization techniques.

Contribution

It presents a novel hybrid LBM that incorporates non-ideal pressure tensor terms and finite difference methods to enhance simulation accuracy and stability for binary fluids.

Findings

Stable algorithm reproduces correct equilibrium behavior

Reduces spurious velocities by about an order of magnitude

Maintains Galilean invariance in simulations

Abstract

A hybrid lattice Boltzmann method (LBM) for binary mixtures based on the free-energy approach is proposed. Non-ideal terms of the pressure tensor are included as a body force in the LBM kinetic equations, used to simulate the continuity and Navier-Stokes equations. The convection-diffusion equation is studied by finite difference methods. Differential operators are discretized in order to reduce the magnitude of spurious velocities. The algorithm has been shown to be stable and reproducing the correct equilibrium behavior in simple test configurations and to be Galilean invariant. Spurious velocities can be reduced of about an order of magnitude with respect to standard discretization procedure.