An unconditionally stable semi-implicit CutFEM for an interaction problem between an elastic membrane and an incompressible fluid

Electronic Transactions on Numerical Analysis

article

Kyle Dunn¹  Roger Lui²  Marcus Sarkis² 

[1] Now at Cold Regions Research and Engineering Laboratory - U.S. Army ERDC;Mathematical Sciences Department, Worcester Polytechnic Institute

关键词: immersed boundary method;    finite element method;    numerical stability;    CutFEM;    unfitted methods;   

DOI  :  10.1553/etna_vol54s296

学科分类：数学（综合）

来源: Kent State University * Institute of Computational Mathematics

【 摘 要 】

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 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.

【 授权许可】

Unknown