Volume 57, Number 3, May-June 2023
|Page(s)||1111 - 1142|
|Published online||08 May 2023|
ϕ-FEM: an optimally convergent and easily implementable immersed boundary method for particulate flows and Stokes equations
MIMESIS Team, INRIA-Institut National de Recherche en Informatique et en Automatique Nancy – Grand Est, MLMS Team, Université de Strasbourg, Strasbourg, France
2 IMAG, Univ Montpellier, CNRS, Montpellier, France
3 Laboratoire de Mathématiques de Besançon, UMR CNRS 6623, Université de Franche-Comté, Besançon, France
* Corresponding author: email@example.com
Accepted: 25 January 2023
We present an immersed boundary method to simulate the creeping motion of a rigid particle in a fluid described by the Stokes equations discretized thanks to a finite element strategy on unfitted meshes, called ϕ-FEM, that uses the description of the solid with a level-set function. One of the advantages of our method is the use of standard finite element spaces and classical integration tools, while maintaining the optimal convergence (theoretically in the H1 norm for the velocity and L2 for pressure; numerically also in the L2 norm for the velocity).
Mathematics Subject Classification: 65N30 / 65N85 / 65N15
Key words: Finite element method / numerical analysis / fictitious domain / immersed boundary method / level-set
© The authors. Published by EDP Sciences, SMAI 2023
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