# Chemical-potential Multiphase Lattice Boltzmann Method with Superlarge Density Ratios

## TL;DR

This paper introduces a chemical-potential multiphase lattice Boltzmann method capable of simulating extremely high liquid-gas density ratios exceeding 10^14, maintaining thermodynamic consistency and high accuracy in dynamic multiphase flows.

## Contribution

The paper develops a novel lattice Boltzmann method that achieves superlarge density ratios with high accuracy and stability, addressing limitations of existing models in multiphase flow simulations.

## Key findings

- Density ratio exceeds 10^14 while preserving thermodynamic consistency
- Suppresses spurious currents to very low levels at high density ratios
- Verifies Galilean invariance through drop splashing simulations

## Abstract

The liquid-gas density ratio is a key property of multiphase flow methods to model real fluid systems. Here, a chemical-potential multiphase lattice Boltzmann method is constructed to realize extremely large density ratios. The simulations show that the method reaches very low temperatures, at which the liquid-gas density ratio is more than 10^14, while the thermodynamic consistency is still preserved. Decoupling the mesh space from the momentum space through a proportional coefficient, a smaller mesh step provides denser lattice nodes to exactly describe the transition region and the resulting dimensional transformation has no loss of accuracy. A compact finite-difference method is applied to calculate the discrete derivatives in the mesh space with high-order accuracy. These enhance the computational accuracy of the nonideal force and suppress the spurious currents to a very low level, even if the density ratio is up to tens of thousands. The simulation of drop splashing verifies that the present model is Galilean invariant for dynamic flow field. An upper limit of the chemical potential is used to reduce the influence of nonphysical factors and improve the stability.

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Source: https://tomesphere.com/paper/1906.09530