Development of a high-order continuous Galerkin sharp-interface immersed boundary method and its application to incompressible flow problems

The sharp-interface immersed boundary method is a strategy to impose boundary conditions on complex geometries while simplifying the meshing process. This method can offer a high-order of accuracy. Most sharp-interface methods have been developed in the context of the finite volume or the finite dif...

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Bibliographic Details
Published in:Computers & fluids 2022-05, Vol.239, p.105415, Article 105415
Main Authors: Barbeau, Lucka, Étienne, Stéphane, Béguin, Cédric, Blais, Bruno
Format: Article
Language:English
Subjects:
Boundary conditions
Context
Couette flow
Drag
Equilibrium flow
Finite difference method
Finite element method
Finite Element Method (FEM)
Fluid flow
Galerkin method
High-order methods
Immersed boundary
Incompressible flow
Navier–Stokes incompressible flow
Sharp interface method
Strouhal number
Unsteady flow
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Summary:The sharp-interface immersed boundary method is a strategy to impose boundary conditions on complex geometries while simplifying the meshing process. This method can offer a high-order of accuracy. Most sharp-interface methods have been developed in the context of the finite volume or the finite difference methods. In this paper, we introduce, verify and validate a novel high-order sharp-interface immersed boundary method in the context of the finite element method. We apply this method to the incompressible Navier–Stokes equations using a pressure-stabilizing/Petrov–Galerkin (PSPG) stabilization. We verify that we obtain a high order of convergence using a Taylor–Couette flow. We validate the results obtained for the drag, lift, and Strouhal number of the flow behind a cylinder at Re=200. We investigate the flow around a sphere at Re=100 and compare the drag force and the characteristics of the recirculating zones with experimental and numerical results obtained in the literature. Finally, the sharp-interface method is used to study a packing of 10 spheres at Re=50, and the results are compared to those obtained with a conformal mesh. It is shown that the sharp-interface immersed boundary preserves the high-order of the finite element scheme and accurately predicts the steady-state and transient flow around particles including the evaluation of the particle-fluid forces. •A novel sharp-interface immersed boundary method for fluid flow is proposed.•It allows the representation of curved geometry without the use of a conformal mesh.•It conserves the order of accuracy of the finite element scheme.•It is validated using relevant 2D/3D experimental and/or numerical results.
ISSN:0045-7930
1879-0747
DOI:10.1016/j.compfluid.2022.105415