Jean-Michel Ghidaglia

Frédéric Dias, Denys Dutykh, Jean-Michel Ghidaglia

In the study of ocean wave impact on structures, one often uses Froude scaling since the dominant force is gravity. However the presence of trapped or entrained air in the water can significantly modify wave impacts. When air is entrained in water in the form of small bubbles, the acoustic properties in the water change dramatically and for example the speed of sound in the mixture is much smaller than in pure water, and even smaller than in pure air. While some work has been done to study small-amplitude disturbances in such mixtures, little work has been done on large disturbances in air-water mixtures. We propose a basic two-fluid model in which both fluids share the same velocities. It is shown that this model can successfully mimic water wave impacts on coastal structures. Even though this is a model without interface, waves can occur. Their dispersion relation is discussed and the formal limit of pure phases (interfacial waves) is considered. The governing equations are discretized by a second-order finite volume method. Numerical results are presented. It is shown that this basic model can be used to study violent aerated flows, especially by providing fast qualitative estimates.

Raphaël Loubère, Jean-Philippe Braeunig, Jean-Michel Ghidaglia

This work concerns the simulation of compressible multi-material fluid flows and follows the method FVCF-NIP described in the former paper Braeunig et al (Eur. J. Mech. B/Fluids, 2009). This Cell-centered Finite Volume method is totally Eulerian since the mesh is not moving and a sharp interface, separating two materials, evolves through the grid. A sliding boundary condition is enforced at the interface and mass, momentum and total energy are conserved. Although this former method performs well on 1D test cases, the interface reconstruction suffers of poor accuracy in conserving shapes for instance in linear advection. This situation leads to spurious instabilities of the interface. The method Enhanced-NIP presented in the present paper cures an inconsistency in the former NIP method that improves strikingly the results. It takes advantage of a more consistent description of the interface in the numerical scheme. Results for linear advection and compressible Euler equations for inviscid fluids are presented to assess the benefits of this new method.