An all-topology two-fluid model for two-phase flows derived through Hamilton's Stationary Action Principle

2025/09/30 by Haegeman, Ward, Orlando, Giuseppe, Kokh, Samuel +1 · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.26298

Abstract

We present a novel multi-fluid model for compressible two-phase flows. The model is derived through a newly developed Stationary Action Principle framework. It is fully closed and introduces a new interfacial quantity, the interfacial work. The closures for the interfacial quantities are provided by the variational principle. They are physically sound and well-defined for all type of flow topologies. The model is shown to be hyperbolic, symmetrizable, and admits an entropy conservation law. Its non-conservative products yield uniquely defined jump conditions which are provided. As such, it allows for the proper treatment of weak solutions. In the multi-dimensional setting, the model presents lift forces which are discussed. The model constitutes a sound basis for future numerical simulations.

Citations

• Two-scale modelling of two-phase flows based on the Stationary Action Principle and a Geometric Method Of Moments
• Transient numerical model of magma ascent dynamics: application to the explosive eruptions at the Soufrière Hills Volcano
• The Cauchy problem for quasi-linear symmetric hyperbolic systems
• A Fundamental Derivative in Gasdynamics
• Symmetric hyperbolic linear differential equations

Cited by

• A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms

Related

• Derivation of a two-phase flow model accounting for surface tension
• Nonequilibrium model for compressible two-phase two-pressure flows with surface tension
• Energetic Variational Approaches for inviscid multiphase flow systems with surface flow and tension
• Two-scale modelling of two-phase flows based on the Stationary Action Principle and a Geometric Method Of Moments
• Thermodynamically consistent modelling and simulation of the moving contact line problem in non-isothermal compressible two-phase flows