Adjoint-Based Optimization for Rigid Body Motion in Multiphase Navier-Stokes Flow

We consider the numerical simulation of rigid body motion in multiphase incompressible Navier-Stokes flow. The motion is formulated as an optimization problem and determined by minimizing an objective function in terms of forces and moments acting on the body, constrained by the multiphase Navier-Stokes equations. The corresponding adjoint system and boundary conditions are derived and derivatives of the objective function are determined. Numerical experiments include the flow around a NACA hydrofoil, a box and the standard benchmark KRISO Container Ship (KCS). We obtain a considerable speedup compared to current state-of-the-art methods.