Entropic multi-relaxation-time lattice Boltzmann model for large density ratio two-phase flows

TL;DR

This paper introduces an entropic multi-relaxation-time lattice Boltzmann model that significantly enhances stability for simulating large density ratio two-phase flows, enabling higher Reynolds numbers and better agreement with theoretical and experimental results.

Contribution

It develops a new entropic multi-relaxation-time lattice Boltzmann model that improves stability and accuracy in large density ratio two-phase flow simulations.

Findings

Enhanced stability limits allowing higher Reynolds numbers.

Good agreement of interface properties with theory.

Accurate simulation of drop impact on liquid films.

Abstract

We propose a multiple relaxation time entropic realization of a two-phase flow lattice Boltzmann model we introduced in earlier works arXiv:2112.01975 S.A. Hosseini, B. Dorschner, and I. V. Karlin, arXiv preprint, arXiv:2112.01975 (2021). While the original model with a single relaxation time allows us to reach large density ratios, it is limited in terms of stability with respect to non-dimensional viscosity and Courant--Friedrichs--Lewy number. Here we show that the entropic multiple relaxation time model extends the stability limits of the model significantly, which allows us to reach larger Reynolds numbers for a given grid resolution. The thermodynamic properties of the solver, using the Peng--Robinson equation of state, are studied first using simple configurations. Co-existence densities and temperature scaling of both the interface thickness and the surface tension are shown to agree well with theory. The model is then used to simulate the impact of a drop onto a thin liquid film with density and viscosity ratios matching those of water and air both in 2-D and 3-D. The results are in very good agreement with theoretically predicted scaling laws and experimental data.