Central-moments-based lattice Boltzmann scheme for coupled Cahn-Hilliard-Navier-Stokes equations

TL;DR

This paper introduces a novel lattice Boltzmann model based on central moments for solving coupled Cahn-Hilliard-Navier-Stokes equations, demonstrating improved stability and accuracy over traditional methods.

Contribution

The paper presents a new LB scheme using central moments for coupled phase-field and fluid flow equations, with direct surface tension force insertion and enhanced stability.

Findings

Achieves high accuracy in benchmark tests

Outperforms BGK approach in stability

Enables simulation of large viscosity contrasts

Abstract

In this paper, we propose a lattice Boltzmann (LB) model to solve the coupled Cahn-Hilliard-Navier-Stokes equations. Differently from previous efforts, the LB equation for the fluid velocity is decomposed in a space of non-orthogonal central moments where the surface tension force is inserted directly in the equilibrium state. The present scheme is validated against well-consolidated benchmark tests, showing very good accuracy. Moreover, it outperforms the BGK approach in terms of stability, as our algorithm allows us to simulate a very large range of viscosity contrast.