The immersed boundary method: Application to two-phase immiscible flows

In this paper we present an extended formulation of the immersed boundary (IB) method that facilitates simulation of incompressible immiscible two-phase flows. In the developed formulation the pressure field and the surface tension forces associated with interface curvature are implicitly introduced in the form of distributed Lagrange multipliers. The approach provides for impermeability between both phases and exhibits accurate mass conservation without the need for additional correction procedures. Further, we present a grid independence study and extensive verification of the developed method for representative 2D two-phase flows dominated by buoyancy, shear stress, and surface tension forces.