An immersed boundary method based on domain decomposition

Abstract

A novel immersed boundary method based on a domain decomposition approach is proposed in the context of a finite element discretisation method. It is applicable to incompressible flows past rigid, deforming, or moving bodies. In this method, unlike most immersed boundary methods, strong boundary conditions are imposed in the regions of the computational domain that are occupied by the structure. In order to achieve this, the proposed formulation decomposes the computational domain by splitting the finite element test functions into solid and fluid parts. In the continuous Galerkin formulation, this produces a smeared representation of the fluid-structure interface. The absence of an immersed boundary forcing term implies that the method itself has no influence on the CFL stability criterion. Furthermore, the stiffness matrix in the momentum equation is sparser than compared with other forcing immersed boundary methods, and symmetry and positive-definiteness of the Laplacian operator in the pressure equation is preserved. As shown in this paper, stability and accurate imposition of boundary conditions make the method promising for high Reynolds number flows. The method is applied to the simulations of two-dimensional laminar flow over stationary and moving cylinders, as well as a moderately high Reynolds number flow past an aerofoil. Good results are obtained when compared with those from previous experimental and numerical studies.