Séance Séminaire

Séminaire MACS

Modelling multiphase compressible flows: subgrid cavitation bubbles and viscoplastic solids

Motivated by applications such as shock wave lithotripsy, we present two complementary numerical frameworks for simulating complex multiscale, multiphase systems. The first framework addresses bubble cluster dynamics by modeling the cluster as a subgrid mixture of gas bubbles and surrounding liquid. Based on a pressure non-equilibrium two-phase model, it employs closures derived from the Keller-Miksis equation to capture spherical bubble dynamics, enabling efficient simulation of collapse and expansion phenomena without resolving each individual bubble. This model extends finite pressure relaxation approaches and is validated through test cases for single bubbles and clusters.

The second framework introduces a diffuse-interface, multiphase Eulerian approach for porous solids interacting with compressible fluids under dynamic loading. Formulated at the mixture level, it incorporates a macroscopic configuration variable decomposed into elastic and plastic parts, and handles large deformations, elastic–plastic behavior, irreversible compaction, and finite-rate pressure relaxation. Thermodynamic consistency is ensured through a generalized standard material framework with convex dissipation potentials and non-negative relaxation multipliers. Together, these frameworks provide the necessary components for simulating complete systems such as those encountered in lithotripsy.