Speaker
Description
Solving fluid-structure interaction problems when the fluid and structure densities are similar (large added mass), as in hemodynamics, is challenging because the stability and convergence properties of the adopted numerical scheme can be compromised. This is especially true for partitioned schemes, whose modularity is otherwise attractive, since it allows exploiting the favorable numerical properties of the sub-problems, which are better conditioned (than the monolithic one), and possibly existing standalone fluid and structural codes. In this regard, the classical Dirichlet–Neumann (DN) coupling scheme, which provides the most natural partitioned formulation of the fluid and structural subproblems, is known to suffer from severe convergence and stability issues in large added-mass regimes.
In this work, we revisit DN coupling from an algebraic viewpoint. Building on its interpretation as a Richardson iteration equipped with a block Gauss–Seidel preconditioner and acceleration parameter α = 1, we design improved coupling strategies suited for large added-mass regimes by considering optimal values of α. We discuss both strongly coupled and loosely coupled formulations, which can be interpreted as preconditioned solvers for the interface problem, and analyze their convergence and stability properties in the presence of large added-mass effects. We further explore strategies to enhance the robustness and practical applicability of these methods. In particular, we investigate automated procedures for selecting stable values of the parameter α, including machine-learning-based approaches, and we study correction strategies to improve the temporal accuracy of the loosely-coupled schemes.
Numerical experiments in hemodynamic settings illustrate the behavior of the proposed methods and highlight their potential as robust preconditioning strategies for coupled multiphysics problems
Acknowledgments
The authors acknowledge their membership in INdAM GNCS.
The authors have been partially supported by the European Union-Next Generation EU, Mission 4, Component 1, CUP: D53D23018770001, research project MIUR PRIN22-PNRR n.P20223KSS2.