An energy-dissipative level-set method for the incompressible two-phase Navier-Stokes equations with surface tension using functional entropy variables

TL;DR

This paper introduces a novel energy-dissipative level-set method for simulating incompressible two-phase Navier-Stokes flows with surface tension, ensuring stability, divergence-free velocity, and density bounds using functional entropy variables.

Contribution

It is the first to develop an energy-dissipative level-set approach based on functional entropy variables for two-phase flow simulations.

Findings

Method is unconditionally energy-dissipative

Velocity field is divergence-free pointwise

Numerical tests confirm stability and accuracy

Abstract

This paper presents the first energy-dissipative level-set method for the incompressible Navier-Stokes equations with surface tension. The methodology relies on the recently proposed concept of functional entropy variables. Discretization in space is performed with isogeometric analysis. Temporal-integration is performed with a new perturbed midpoint scheme. The fully-discrete scheme is unconditionally energy-dissipative, pointwise divergence-free and satisfies the maximum principle for the density. Numerical examples in two and three dimensions verify the energetic-stability of the methodology.