A General, Mass-Preserving Navier-Stokes Projection Method

TL;DR

This paper introduces a novel projection method for multiphase fluid simulations that ensures mass conservation both locally and globally, effectively handling complex morphological changes.

Contribution

A new mass-preserving projection method for Navier-Stokes equations that maintains mass conservation during complex fluid interface dynamics.

Findings

Successfully conserves mass in various fluid scenarios

Handles droplet breakup and morphological changes effectively

Uses an efficient Schur-complement solver

Abstract

The conservation of mass is common issue with multiphase fluid simulations. In this work a novel projection method is presented which conserves mass both locally and globally. The fluid pressure is augmented with a time-varying component which accounts for any global mass change. The resulting system of equations is solved using an efficient Schur-complement method. Using the proposed method four numerical examples are performed: the evolution of a static bubble, the rise of a bubble, the breakup of a thin fluid thread, and the extension of a droplet in shear flow. The method is capable of conserving the mass even in situations with morphological changes such as droplet breakup.