An energy-preserving level set method for multiphase flows

TL;DR

This paper introduces an energy-preserving level set method for multiphase flows that maintains the mechanical energy balance, improving the physical accuracy of interface simulations.

Contribution

It proposes a novel discretization strategy for curvature that conserves total mechanical energy, inspired by symmetry-preserving and mimetic schemes.

Findings

The method ensures conservation of total mechanical energy in simulations.

Numerical tests demonstrate the robustness of the energy-preserving scheme.

The approach improves physical fidelity in multiphase flow modeling.

Abstract

The computation of multiphase flows presents a subtle energetic equilibrium between potential (i.e., surface) and kinetic energies. The use of traditional interface-capturing schemes provides no control over such a dynamic balance. In the spirit of the wellknown symmetry-preserving and mimetic schemes, whose physics-compatible discretizations rely upon preserving the underlying mathematical structures of the space, we identify the corresponding structure and propose a new discretization strategy for curvature. The new scheme ensures conservation of mechanical energy (i.e., surface plus kinetic) up to temporal integration. Inviscid numerical simulations are performed to show the robustness of such a method.