Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Ward Haegeman, Giuseppe Orlando, Samuel Kokh, Marc Massot

TL;DR

The paper addresses the need for a robust, all-topology, compressible two-fluid model capable of handling shocks and topology changes without interface tracking. It develops a two-trajectory Stationary Action Principle framework that yields a fully closed system with new interfacial work and a mass-weighted interfacial velocity $u=Y_1u_1+Y_2u_2$, producing an interfacial pressure $p_I=Y_2p_1+Y_1p_2$ and a momentum-exchange term that preserves total momentum and energy. In 1D, the model is hyperbolic and symmetrizable under a non-resonance condition, admits a conservative entropy equation to select admissible shocks, and provides well-defined jump conditions for weak solutions; in 2D, lift forces arise via a new potential velocity $\mathbf{v}=\nabla\zeta$, with $\rho\mathrm{D}_t\zeta=p_1-p_2$, indicating rich interfacial dynamics that warrant further study. The work offers a physically consistent, mathematically well-posed foundation for future numerical simulations of complex two-phase flows, including potential reductions and Riemann-solver development.

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.

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

TL;DR

The paper addresses the need for a robust, all-topology, compressible two-fluid model capable of handling shocks and topology changes without interface tracking. It develops a two-trajectory Stationary Action Principle framework that yields a fully closed system with new interfacial work and a mass-weighted interfacial velocity , producing an interfacial pressure and a momentum-exchange term that preserves total momentum and energy. In 1D, the model is hyperbolic and symmetrizable under a non-resonance condition, admits a conservative entropy equation to select admissible shocks, and provides well-defined jump conditions for weak solutions; in 2D, lift forces arise via a new potential velocity , with , indicating rich interfacial dynamics that warrant further study. The work offers a physically consistent, mathematically well-posed foundation for future numerical simulations of complex two-phase flows, including potential reductions and Riemann-solver development.

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.

Paper Structure

This paper contains 17 sections, 85 equations.

Table of Contents

  1. Introduction
  2. The Stationary Action Principle with two families of trajectories
  3. An all-topology two-phase flow model
  4. Derivation of the model
  5. Analysis of the interfacial quantities
  6. Multi-dimensional effects
  7. Modelling source terms
  8. Mathematical analysis of the model: the one-dimensional setting
  9. Hyperbolicity and characteristic fields
  10. Riemann invariants and jump conditions
  11. Symmetrization
  12. Some comments on the multi-dimensional case
  13. Conclusion
  14. Derivation of the generic system through Stationary Action principle
  15. Proof of Theorem \ref{['thrm:SAP']}
  16. ...and 2 more sections

Theorems & Definitions (5)

  • proof
  • proof
  • proof
  • proof
  • proof