An Immersed Interface Method for the Simulation of Coupled Fluid-Body Problems

We present a finite-difference immersed interface method (IIM) for the simulation of coupled fluid-body problems, formulated using the velocity-vorticity form of the 2D Navier Stokes equations. Using conservative finite-difference schemes our approach can enforce circulation conservation around each separate body in the domain, even when using outflow boundary conditions. Moving boundaries and emerging points are handled naturally in the IIM framework, even with high-order timestepping. For two-way coupling problems, where the body motion is driven by hydrodynamic forces, we use a control volume approach to enforce a momentum balance. The method achieves second-order convergence for most practical simulations except those involving small density ratios, where a first-order error term related to our two-way coupling approach dominates. We show the ability of this approach to accurately and efficiently run long-time simulations with compact domains and circulation conservation on several benchmark and convergence studies.