Spurious currents suppression by accurate difference schemes in multiphase lattice Boltzmann method

TL;DR

This paper investigates the causes of spurious currents in multiphase lattice Boltzmann simulations and demonstrates that high-order finite difference schemes significantly reduce these unphysical phenomena, improving accuracy and stability.

Contribution

It compares various finite difference schemes, showing high-order methods effectively suppress spurious currents and enhance simulation accuracy in multiphase lattice Boltzmann methods.

Findings

High-order finite difference schemes reduce spurious currents.

Simulation results align well with theoretical predictions.

3D and 2D results are highly consistent.

Abstract

Spurious currents, which are often observed near a curved interface in the multiphase simulations by diffuse interface methods, are unphysical phenomena and usually damage the computational accuracy and stability. In this paper, the origination and suppression of spurious currents are investigated by using the multiphase lattice Boltzmann method driven by chemical potential. Both the difference error and insufficient isotropy of discrete gradient operator give rise to the directional deviations of nonideal force and then originate the spurious currents. Nevertheless, the high-order finite difference produces far more accurate results than the high-order isotropic difference. We compare several finite difference schemes which have different formal accuracy and resolution. When a large proportional coefficient is used, the transition region is narrow and steep, and the resolution of finite difference indicates the computational accuracy more exactly than the formal accuracy. On the contrary, for a small proportional coefficient, the transition region is wide and gentle, and the formal accuracy of finite difference indicates the computational accuracy better than the resolution. Furthermore, numerical simulations show that the spurious currents calculated in the 3D situation are highly consistent with those in 2D simulations; especially, the two-phase coexistence densities calculated by the high-order accuracy finite difference are in excellent agreement with the theoretical predictions of the Maxwell equal-area construction till the reduced temperature 0.2.