φ-FEM: an optimally convergent and easily implementable immersed boundary method for particulate flows and Stokes equations

Michel Duprez (1, 2) , Vanessa Lleras (3) , Alexei Lozinski (4, 5)

1 MIMESIS - Computational Anatomy and Simulation for Medicine
2 ICube - Laboratoire des sciences de l'ingénieur, de l'informatique et de l'imagerie
3 IMAG - Institut Montpelliérain Alexander Grothendieck
4 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
5 MATHERIALS - MATHematics for MatERIALS

We present an immersed boundary method to simulate the creeping motion of a solid in a fluid thanks to the Stokes equation and a FEM element strategy called φ-FEM using 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. We obtain the optimal convergence of the method theoretically and numerically.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Michel Duprez, Vanessa Lleras, Alexei Lozinski. φ-FEM: an optimally convergent and easily implementable immersed boundary method for particulate flows and Stokes equations. 2022. ⟨hal-03588715v1⟩