Thermodynamically-stable diffuse-interface multiscale methods, with applications to sloshing flows

• Applicant: Dr. Marco ten Eikelder
• Subject Area: Fluid Mechanics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 566600860

Robust computer simulations of incompressible multi-fluid flows pose high requirements on two components, namely the interface description as well as the modeling of small-scale effects. Existing computational techniques for single-fluid turbulent flows are well studied, but their extension to the challenging multi-fluid problems remains largely unexplored. This is primarily due to the interaction of the two components; small-scale effects can change the topological structure of the interface. The proposed project is based on the hypothesis that a thermodynamically stable multi-fluid multi-scale methodology can significantly improve the simulation quality of turbulent multi-fluid flows. To this purpose, we will combine the recently proposed consistent Navier-Stokes Cahn-Hilliard (NSCH) model with the variational multiscale (VMS) method. This NSCH model captures topological transitions through the diffuse-interface description, and is the first thermodynamically-stable model that naturally emerges from continuum mixture theory. On the other hand, the VMS constitutes a promising tool for the finite element simulation of turbulent flows, in which practical mesh widths cannot resolve tiny turbulent eddies. In this project we will merge the NSCH model with the VMS method to a design a computational framework for sloshing flows that accurately accounts for small-scale effects at the fluid interface. The novel approach will be integrated into modern discretization techniques based on higher-order isogeometric finite element methods. Its performance in terms of accuracy and robustness and its potential in industrial applications will be investigated and demonstrated using challenging sloshing simulations.

• DFG Programme: Research Grants
• International Connection: United Kingdom, USA
• Cooperation Partners: Professor Hector Gomez; Professor Kristoffer van der Zee, Ph.D.