An unconditionally stable semi-implicit CutFEM for an interaction problem between an elastic membrane and an incompressible fluid
For computational fluid-structure interaction, this method removes stability constraints, enabling robust simulations on non-aligned structured meshes.
The paper introduces a CutFEM for Stokes flow with an immersed elastic membrane, achieving unconditional energy stability without parameter restrictions that limited prior methods. Numerical simulations confirm the theoretical stability results.
In this paper we introduce a finite element method for the Stokes equations with a massless immersed membrane. This membrane applies normal and tangential forces affecting the velocity and pressure of the fluid. Additionally, the points representing this membrane move with the local fluid velocity. We design and implement a high-accuracy cut finite element method (CutFEM) which enables the use of a structured mesh that is not aligned with the immersed membrane and then we formulate a time discretization that yields an unconditionally energy stable scheme. We prove that the stability is not restricted by the parameter choices that constrained previous finite element immersed boundary methods and illustrate the theoretical results with numerical simulations.