<i>ϕ</i>-FEM: an optimally convergent and easily implementable immersed boundary method for particulate flows and Stokes equations
Michel Duprez, Vanessa Lleras, Alexei Lozinski
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 H 1 norm for the velocity and L 2 for pressure; numerically also in the L 2 norm for the velocity).
Topics & Concepts
Finite element methodDiscretizationNorm (philosophy)Stokes flowConvergence (economics)Polygon meshMathematical analysisExtended finite element methodBoundary (topology)MathematicsPressure-correction methodStokes problemBoundary value problemApplied mathematicsGeometryPhysicsEconomicsThermodynamicsFlow (mathematics)LawEconomic growthPolitical scienceLattice Boltzmann Simulation StudiesHeat and Mass Transfer in Porous MediaFluid Dynamics Simulations and Interactions