Fluid-Structure Interaction (FSI) problems, which describe the dynamic interplay between a fluid and a solid, present significant mathematical challenges due to the complex coupling at the FSI interface. This interface, shared by the fluid and solid subdomains, evolves based on the dynamics of both, making its profile unknown a priori. Despite extensive research, a unified mathematical approach to FSI remains elusive, partly due to the intricate nature of the Navier-Stokes and elastic solid equations that govern the problem.
Traditionally, FSI problems are tackled using either partitioned or monolithic approaches. Partitioned algorithms leverage existing computational tools for fluid and structural dynamics, coupled through iterative procedures, while monolithic algorithms solve the coupled problem simultaneously by imposing global fluid-structure spaces. Although partitioned approaches are computationally advantageous and highly parallelisable, they often suffer from stability and convergence issues, particularly due to the "added-mass" effect common in cardiovascular applications.
This seminar introduces a novel partitioned algorithm designed to maintain stability under the “added-mass” effect. We will begin by discussing the physical foundations of the model and presenting a consistent variational formulation using the Arbitrary Lagrangian-Eulerian (ALE) framework. The focus will then shift to an optimisation-based domain decomposition (DD) model that ensures the coupling of interface conditions between fluid and structure subdomains. We will explore the resulting optimal-control problem and introduce effective iterative minimisation algorithms that facilitate a complete separation of the subproblems.
Given the complexity of FSI problems and the need for very small-time steps to achieve numerical convergence, the second part of the talk will present a custom local time estimator for pressure-dominated flows, which are particularly challenging due to the differential-algebraic structure of the fluid subproblem. Next, we will discuss incorporating time-adaptivity into the previously presented DD model. This entails a search for more effective (and possibly novel) optimisation algorithms and acceleration techniques capable of overcoming the local and slow convergence of classical minimisation methods.
The seminar will conclude with a discussion of open questions and future research directions, inviting a productive exchange of ideas.
Join at: imt.lu/sagrestia