φ-FEM: an optimally convergent and easily implementable immersed boundary method for particulate flows and Stokes equations - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles ESAIM: Mathematical Modelling and Numerical Analysis Year : 2023

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

Abstract

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).
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Dates and versions

hal-03588715 , version 1 (08-03-2022)
hal-03588715 , version 2 (02-11-2022)
hal-03588715 , version 3 (13-11-2022)
hal-03588715 , version 4 (27-01-2023)

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Cite

Michel Duprez, Vanessa Lleras, Alexei Lozinski. φ-FEM: an optimally convergent and easily implementable immersed boundary method for particulate flows and Stokes equations. ESAIM: Mathematical Modelling and Numerical Analysis, 2023, 57, pp.1111-1142. ⟨10.1051/m2an/2023010⟩. ⟨hal-03588715v4⟩
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