COPERNICUS · COmpatible hyPERbolic models and advanced NumerIcs for Compressible multiphase flows on UnStructured meshes

Multiphase flows, where liquids, gases, and solids interact, are ubiquitous in nature and industry. Modeling such flows accurately is fundamental to progress in fields such as aerospace, biomedical, and environmental engineering fields. Existing models for multiphase flows, such as Baer-Nunziato, Kapila, and Romenski, are widely used, but they have limited application and do not allow taking into account important features such as surface tension, phase transition, or elastic interactions of materials.The main objective of COPERNICUS is to formulate a novel hyperbolic and thermodynamically compatible (HTC) model for multiphase flows, which incorporates the effects of surface tension, phase changes, and elastic interactions between phases. The new model, derived from variational principles, will ensure energy conservation, thermodynamic compatibility, and hyperbolicity. In addition, new high-order, structure-preserving numerical methods will be developed to simulate complex real-world phenomena that can be observed in the real world accurately and efficiently. This project will significantly advance the field, offering a unified framework for modeling a wider range of multiphase interactions.Secondments at the University of Aix-Marseille, with Professor Gavrilyuk, and at the University of Trento, under the supervision of Professor Dumbser, will complement the theoretical and numerical foundation needed to achieve the project's ambitious goals.For the fellow, this project will provide valuable professional experience. She will improve her mathematical modeling, numerical methods, and parallel computing knowledge. Beyond scientific skills, she will also receive training in project management, leadership, and open science practices, which will prepare her for a future career as an independent researcher.