An efficient quasi-Newton method for two-dimensional steady free surface flow

Steady free surface flows are of interest in the fields of marine and hydraulic engineering. Fitting methods are generally used to represent the free surface position with a deforming grid. Existing fitting methods tend to use time-stepping schemes, which is inefficient for steady flows. There also exists a steady iterative method, but that one needs to be implemented with a dedicated solver. Therefore a new method is proposed to efficiently simulate two-dimensional (2D) steady free surface flows, suitable for use in conjunction with black-box flow solvers. The free surface position is calculated with a quasi-Newton method, where the approximate Jacobian is constructed in a novel way by combining data from past iterations with an analytical model based on a perturbation analysis of a potential flow. The method is tested on two 2D cases: the flow over a bottom topography and the flow over a hydrofoil. For all simulations the new method converges exponentially and in few iterations. Furthermore, convergence is independent of the free surface mesh size for all tests.