Numerical solution of steady free-surface Navier-Stokes flow

Numerical solution of flows that are partially bounded by a freely moving boundary is of great practical importance, e.g., in ship hydrodynamics. The usual time integration approach for solving steady viscous free surface flow problems has several drawbacks. Instead, we propose an efficient iterative method, which relies on a different but equivalent formulation of the free surface flow problem, involving a so-called quasi free-surface condition. It is shown that the method converges if the solution is sufficiently smooth in the neighborhood of the free surface. Details are provided for the implementation of the method in {PARNAX. Furthermore, we present a method for analyzing properties of discretization schemes for the free-surface flow equations. Detailed numerical results are presented for flow over an obstacle in a channel. The results agree well with measurements as well as with the predictions of the analysis, and confirm that steady free-surface Navier-Stokes flow problems can indeed be solved efficiently with the new method.