An all-topology two-fluid model for two-phase flows derived through Hamilton’s Stationary Action Principle
The goal here is to demonstrate the feasability of numerical simulations of a new all-topology two-fluid model (Haegeman et al. 2025) using a standard first-order finite-volume scheme.
Hereafter, we provide the abstract of the contribution in which the model is derived, as well as a link to the full preprint.
Next, details on the numerical scheme used and its implementation using the open-source Samurai library are given before listing the numerical test cases.
At the end of this web-page, all the information necessary to install and run the code in order to reproduce the numerical data can be found.
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.
Preprint available at HAL-05249139
Numerical method and implementation
The model has been implemented without the contributions related to the lift forces. We refer to (Haegeman et al. 2025) for a complete description of the model. Our implementation corresponds to a finite volume method on structured meshes represented by cartesian grids. On each inter-cell interface, the numerical flux is computed using an approximate Rieman solver. Here, we use the first-order non-conservative Rusanov scheme presented in (Crouzet et al. 2013). Under a standard CFL condition, the scheme is positivity-preserving for the volume fraction and phasic densities.
List of test cases
Three types of test cases are available, a one-dimensional Riemann problem and a two-dimensional Riemann problem.
You can access the test cases using the links below or through the navigation bar on the left.
Data reproducibility
Please, find the source codes and post-processing scripts used to generate the data at
https://github.com/hpc-maths/2025_09_two_fluid_all_topology
We refer to Samurai for the installation of the library.