phi-FEM for creeping flows around moving particles

  • Duprez, Michel (Inria, MLMS team)
  • Lleras, Vanessa (IMAG, Univ. Montpellier)
  • Lozinski, Alexei (Laboratoire de mathématiques de Besançon)

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We shall present an immersed boundary method [1] to simulate the creeping motion of rigid particles in the Newtonian fluid using finite elements on unfitted meshes. Our strategy, called phi-FEM, uses the description of the solid by a level-set function and introduces this function into the variational setting. Our method employs the standard finite element spaces and the straightforward numerical integration, while maintaining the optimal convergence orders for the for the velocity and pressure. We shall also discuss an extensions to the case of elastic particles. [1] M. Duprez, V. Lleras, A. Lozinski. phi-FEM: an optimally convergent and easily implementable immersed boundary method for particulate flows and Stokes equations. To appear in M2AN, 2023.