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ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis, pp. 296-322, 2021/04/15
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.
Keywords: immersed boundary method, finite element method, numerical stability, CutFEM, unfitted methods