Numerical solution of flows that are partially bounded by a freely moving boundary is of great importance in practical applications such as ship hydrodynamics. The usual method for solving steady viscous free-surface flow subject to gravitation is alternating time integration of the kinematic condition, and the Navier-Stokes equations with the dynamic conditions imposed, until steady state is reached. This paper shows that at subcritical Froude numbers this time integration approach is necessarily inefficient and proposes an efficient iterative method for solving the steady free-surface flow problem. The new method relies on a different but equivalent formulation of the free-surface flow problem, involving a so-called quasi free-surface condition. The convergence behavior of the new method is shown to be asymptotically mesh width independent. Numerical results are presented for 2D flow over an obstacle in a channel. The results confirm the mesh width independence of the convergence behavior and comparison of the numerical results with measurements shows good agreement.

Stability and convergence of numerical methods (msc 65N12), Free boundary problems (msc 35R35), Navier-Stokes equations (msc 76D05), Other free-boundary flows; Hele-Shaw flows (msc 76D27), Waves (msc 76D33)
Life Sciences (theme 5), Energy (theme 4)
Modelling, Analysis and Simulation [MAS]
Scientific Computing

van Brummelen, E.H, Raven, H.C, & Koren, B. (2001). Efficient numerical solution of steady free-surface Navier-Stokes flow. Modelling, Analysis and Simulation [MAS]. CWI.