Energetic Variational Approaches for inviscid multiphase flow systems with surface flow and tension

TL;DR

This paper develops energetic variational methods to derive and analyze inviscid multiphase flow systems with surface flow and tension, focusing on conservation laws and pressure formulations.

Contribution

It introduces a novel energetic variational framework for modeling inviscid multiphase flows with surface effects, including new derivations of pressure on surfaces.

Findings

Derived multiphase flow equations with surface tension using variational methods

Established conservation and energy laws for the proposed flow systems

Provided new insights into pressure formulations on moving surfaces

Abstract

We consider the governing equations for the motion of the inviscid fluids in two moving domains and an evolving surface from an energetic point of view. We employ our energetic variational approaches to derive inviscid multiphase flow systems with surface flow and tension. More precisely, we calculate the variation of the flow maps to the action integral for our model to derive both surface flow and tension. We also study the conservation and energy laws of our multiphase flow systems. The key idea of deriving the pressure of the compressible fluid on the surface is to make use of the feature of the barotropic fluid, and the key idea of deriving the pressure of the incompressible fluid on the surface is to apply a generalized Helmholtz-Weyl decomposition on a closed surface.