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

2018/01/17 by Kyle Dunn, Dunn, Kyle, Roger Lui +3
Computer Science · Engineering · Physics and Astronomy · #65N12 #65N30 #74F10 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Lattice Boltzmann Simulation Studies #Micro and Nano Robotics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1801.05794

openalex publication_date 2018/01/17 · openalex created_date 2022/08/17 · openalex updated_date 2026/07/28

Abstract

In this paper we introduce a finite element method for the Stokes equations\nwith a massless immersed membrane. This membrane applies normal and tangential\nforces affecting the velocity and pressure of the fluid. Additionally, the\npoints representing this membrane move with the local fluid velocity. We design\nand implement a high-accuracy cut finite element method (CutFEM) which enables\nthe use of a structured mesh that is not aligned with the immersed membrane and\nthen we formulate a time discretization that yields an unconditionally energy\nstable scheme. We prove that the stability is not restricted by the parameter\nchoices that constrained previous finite element immersed boundary methods and\nillustrate the theoretical results with numerical simulations.\n

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