An Adaptive Mesh Algorithm for Free Surface Flows in General Geometries

The error is largest in regions near the free surface. A finer mesh is needed at the free surface more than elsewhere. There are quite a few numerical techniques for implementing adaptivity. In the finite element framework, the reader is referred to the following works [47, 37, 19, 9, 35, 63, 30, 36]. In the finite difference framework(i.e., uniform rectangular mesh), the reader is referred to the following dynamic adaptive grid methods [6, 1, 48, 62, 34]. Other methods that allow one to add grid resolution where needed are so-called Overset-grid methods [13, 18].