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 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.

Uncontrolled Keywords

• Sharp interface method
• Finite Element Method (FEM)
• Immersed boundary
• High-order methods
• Navier–Stokes incompressible flow