An Energy Stable Nonlinear Incompressible Multi-Phase Flow Formulation

TL;DR

This paper introduces a reformulated incompressible multi-phase flow model that guarantees energy stability through a new mathematical approach, enabling more reliable simulations of complex fluid interactions.

Contribution

The paper presents a novel reformulation of governing equations that ensures nonlinear energy stability using summation-by-parts operators, advancing the modeling of multi-phase flows.

Findings

Energy rate is well-defined in the new formulation.

Boundary conditions support energy estimates.

The approach achieves provable nonlinear energy stability.

Abstract

We show that a reformulation of the governing equations for incompressible multi-phase flow in the volume of fluid setting leads to a well defined energy rate. Weak nonlinear inflow-outflow and solid wall boundary conditions complement the development and lead to an energy estimate in terms of external data. The new formulation combined with summation-by-parts operators lead to provably nonlinear energy stability.