Implementation of a discrete Immersed Boundary Method in OpenFOAM

Abstract: In this paper, the Immersed Boundary Method (IBM) proposed by Pinelli is implemented for finite volume approximations of incompressible Navier-Stokes equations solutions in the open source toolbox OpenFOAM version 2.2. Solid obstacles are described using a discrete forcing approach for boundary conditions. Unlike traditional approaches encompassing the presence of a solid body using conformal meshes and imposing no-slip boundary conditions on the boundary faces of the mesh, the solid body is here represented on the Eulerian Cartesian mesh through an ad-hoc body force evaluated on a set of Lagrangian markers. The markers can move across the Eulerian mesh, hence allowing for a straightforward analysis of motion or deformation of the body. The IBM method is described and implemented in PisoFOAM, whose Pressure-Implicit Split-Operator (PISO) solver is modified accordingly. The presence of the solid body and the divergence-free of the fluid velocity are imposed simultaneously by sub-iterating between IBM and the pressure correction step. This scheme allows for the use of fast optimized Poisson solvers while granting excellent accuracy with respect to the previously mentioned constraints. Various 2D and 3D well-documented test cases of flows around fixed or moving circular cylinders are simulated and carefully validated against existing data from the literature. The capability of the new solver is discussed in terms of accuracy and numerical performances.