Development of a high-order continuous Galerkin sharp-interface immersed boundary method and its application to incompressible flow problems. (15th May 2022)

• Record Type: Journal Article
• Authors: Barbeau, Lucka; Étienne, Stéphane; Béguin, Cédric; Blais, Bruno
• Is Part Of: Computers & fluids. Volume 239(2022)
• Publication Date: 2022-05-15
• Subjects: Sharp interface method -- Finite Element Method (FEM) -- Immersed boundary -- High-order methods -- Navier–Stokes incompressible flow; Fluid dynamics -- Data processing -- Periodicals; 532.050285
• DOI: 10.1016/j.compfluid.2022.105415
• Languages: English
• ISSNs: 0045-7930

Abstract

Abstract: 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 R e = 200 . We investigate the flow around a sphere at R e = 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 R e = 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. Highlights: 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.