Adaptive Overlapping Grid Techniques and Spatial Discretization Schemes for Increasing Surface Sharpness and Numerical Accuracy in Free Surface Capturing Methods.

Orych, Michal, Lars Larsson, and Björn Regnström.

28th Symposium on Naval Hydrodynamics, Pasadena, California, USA, 12-17 September 2010.


This paper is a result of investigations carried out during the implementation of a free surface capturing method in a RANS solver. The work consists of two distinct parts which complement each other, and the purpose is to improve the free surface interface sharpness and to reduce numerical diffusion of the gravity waves. The first part deals with numerical schemes and the second with local grid refinement and adaptivity near the interface. There is a vast amount of discretization schemes for convection equations. However, only a subset is found to be applicable to the water fraction transport equation. Here we investigate the performance of selected schemes applied to hydrodynamic problems. Moreover, an additional scheme is developed based on the experience gained during the work. This part of the work was carried out since there is very little information in the literature for problems beyond academic test cases such as bubble convection or two dimensional shape translation and rotation. The second part of the presented work concerns air-water interface refinements using fixed and adaptive overlapping grids. The adaptive refinement grid follows approximately the free surface interface and reduces the refinement thickness, thus reducing the required number of discretization cells. The grid alignment with the interface reduces further the diffusion of the water fraction in the transition region from air to water. The work carried out has led to a well performing and simple to implement scheme for the water fraction transport equation. Adaptive overlapping refinement grids have proved to be a less robust solution at this stage, however the fixed local refinements can already be used with confidence.