A conservative level-set method based on a posterior mass correction preserving distance property for incompressible multiphase flows simulations

TL;DR

This paper introduces a conservative level-set method with a posterior mass correction that preserves the signed distance property, significantly improving mass conservation in multiphase flow simulations with minimal computational overhead.

Contribution

A novel mass correction technique for level-set methods that maintains the signed distance property and enhances mass conservation without substantial computational cost.

Findings

Mass conservation error reduced to machine precision

Method preserves signed distance property after correction

Applicable to both 2D and 3D multiphase flow simulations

Abstract

As one of the most popular interface-capturing methods, the level-set method is inherently non-conservative, and its evolution usually leads to unphysical mass gain/loss. In this paper, a novel conservative level set method is developed for incompressible multiphase flows simulations. A posterior mass correction is performed by introducing a small perturbation to the level-set field, which is solved via the Newton method. Unlike in previous researches, the signed distance property of the level-set function is exactly preserved after the present mass correction. Moreover, this method can be easily generalized from 2D to 3D. The influence for the computational efficiency is slight as the correction does not need to be applied at every time step. Various benchmark cases involving pure interface-evolution problems and multiphase flows problems are considered to validate the present method. For all cases, the accuracy and efficiency of the original method and the present method are quantitatively compared. It is observed that, with negligibly extra cost, the conservation error is reduced to the order of machine accuracy by the present method, which indicates its potential applications in complex multiphase flows simulations.