ON THE IMMERSED BOUNDARY METHOD: FINITE ELEMENT VERSUS FINITE VOLUME APPROACH

A projection approach is presented for the coupled system of time-dependent incompressible Navier-Stokes equations in conjunction with the Immersed Boundary Method (IBM) for solving fluid flow problems in the presence of rigid objects not represented by the underlying mesh. The IBM allows solving the flow for geometries with complex objects without the need of generating a body fitted mesh. The no-slip boundary constraint is satisfied applying a boundary force at the immersed body surface. Using projection and interpolation operators from the fluid volume mesh to the solid surface mesh (i.e., the “immersed ” boundary) and vice versa, it is possible to impose the extra constraint to the incompressible Navier-Stokes equations as a Lagrange multiplier in a fashion very similar to the effect pressure has on the momentum equations to satisf