New techniques for solving the steady free surface flow problem

Steady free surface (FS) flows can be solved numerically with capturing or fitting methods, the latter being the subject of this paper. Most fitting methods are (pseudo-)transient and thus quite slow for steady flows; the so-called steady iterative method is much faster, but requires a dedicated solver because of the complex FS boundary conditions. The goal is to develop a (currently 2D) fitting method which is fast and can be used with a black box flow solver. Results from a perturbation analysis are used in combination with the IQN-ILS algorithm to construct such a method, applicable to supercritical flows. To tackle this method's scaling problem when the mesh is refined, an extension is proposed which uses a multigrid technique for the surface update. The flow over an object is simulated with the original and multigrid enhanced methods for three meshes. The multigrid method clearly outperforms the original one and is even mesh independent during part of its convergence.