NextGenFSI

Matematička teorija nove generacije modela interakcije fluida i struktura

Research project financed by Croatian Science Foundation

Project Summary:

Fluid-structure interactions (FSI) are ubiquitous in nature and technology. Mathematically, they are described by a coupled nonlinear system of partial differential equations. For instance, the Navier-Stokes equations are coupled to elasto-dynamics across the moving interface. Motivated by a plethora of applications ranging from biomedicine to nanotechnology, the last few decades have been a very active research period in FSIs. Significant progress has been made with many deep results in analysis, scientific computing and modeling. However, very important questions such as topological changes of the fluid domain (self-intersections and contact) and regularity of the interface remain unresolved and create a bottleneck that prevents further developments and applicability of models. Nevertheless, next generation of applications, particularly in biomedicine (for example design of artificial pancreas), requires an upgrade of standard FSI models to take into account porosity of the structure and to allow some fluid filtration through it. This project aims to develop a comprehensive unified FSI theory, which will facilitate design and analysis of corresponding numerical schemes. The key to our approach is to consider more general versions of FSI problems, which are based on the interplay between two novel concepts in the context of FSI: a diffuse interface and a poroelastic solid. The idea of the former is to replace the interface by a thin transition region between the fluid and the solid phase, which is intimately related with the fluid filtration through the solid phase, thus giving rise to a poroelastic model for the structure. This generalization will be justified by showing that classical FSI problems and relevant reduced FSI models can be recovered as singular limits in suitable parameter regimes. In the numerical computations we will combine classical finite elements methods with recent advances in deep neural networks.