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arXiv · 2509.26298

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
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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 types 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.

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Ward Haegeman, Giuseppe Orlando, Samuel Kokh, Marc Massot. 2025-09-30. An all-topology two-fluid model for two-phase flows derived through Hamilton's Stationary Action Principle. https://doi.org/10.1098/rspa.2025.0835

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