Combined refinement criteria for anisotropic grid refinement in free-surface flow simulation

• The paper studies grid refinement for realistic free-surface hydrodynamic flows.
• Good refinement criteria are a combination of free-surface and derivative-based ones.
• Refinement criteria based on the pressure Hessian need to contain smoothing.
• Ratio of two criteria is set independent of scaling, Froude or Reynolds number.
• Fine meshes of good quality are generated entirely with automatic grid refinement.

Anisotropic grid refinement is performed for the simulation of water flow with free-surface waves. For these flows, the refinement criterion must provide refinement at the water surface, to accurately resolve the conservation law which indicates the surface position, and below the surface to resolve the water flow. A combined criterion is presented, based on the free-surface position and on the Hessian of the pressure. Different forms of this criterion are presented, based on least-squares or Gaussian computation of the Hessian, in order to overcome irregularities in the computed pressure. The weighting of the two criteria for their combination is discussed; this weighting can be chosen independently of the Reynolds and Froude number of the flow. It is shown that the criterion creates suitable grids for two- and three-dimensional free-surface flows when starting from uniformly coarse original grids.