An immersed interface vortex method for internal and external 2D flows with moving boundaries

We present a novel Immersed Interface Method for 2D viscous incompressible flows. The vorticity-velocity form of the Navier-Stokes equations are discretized using second-order conservative finite differences and third-order explicit time integration. The discretization and interface treatment can handle both internal and external flows, and both stationary and moving boundaries. For external flows, the use of a vorticity-based formulation allows free-space boundary conditions while only discretizing the compact support of the vorticity field. We further show how the sharp treatment of the boundary provides a natural and accurate way to compute pressure and viscous force distributions on stationary and moving obstacles. Our method is ideal for unsteady aero- and hydrodynamic problems, and we demonstrate its utility through simulations of cylinder arrays, heaving/pitching foils, and kinematically-driven internal flows.