Orateur
Description
In the context of multiphysics simulations, partitioned methods enable the reuse of existing solvers while preserving modularity. However, achieving high-order accuracy in time and providing adaptive time stepping remains a challenge, especially when dealing with strong coupling conditions. We address these issues by developing and analyzing a high-order multistep coupling scheme tailored for multiphysics applications. Contrary to classical staggered coupling schemes, where the coupling terms are held constant between two successive coupling time points, this new technique uses high-order polynomial-in-time predictions of the evolution of the coupling conditions during a coupling time step. An explicit and an implicit variants arise naturally, and error estimates can be built to dynamically drive the coupling timestep. I will present a numerical analysis of convergence and stability of the multistep coupling scheme.