Comparative Evaluation of Numerical Methods in Free-Surface Hydrodynamics

摘要

The subject of free-surface and body interaction is characterized by a set of boundary-value problems that is well-established, but defies simple analytical treatment except for the simplest body geometry. In most problems of practical interest, the need for numerical solutions exists. This paper considers the nature and means of such numerical approximations of the exact solutions. An expository review is given on 3 major types of numerical methods commonly used in free-surface and body interaction problems of the deterministic type. General principles governing boundary-fitted coordinates are described. Formulations commonly used for finite-element type methods are explained. Boundary-integral equation methods of various forms are discussed. Special attention is paid to features of each type of method that are efficient and potentially attractive and also to features that are known to be problematic. Various current research activities in time-dependent type solutions are briefly summarized. A novel idea involving the new concept of 'shell functions' in unsteady problems is proposed. Once properly calculated, the 'shell coefficients' can be used for a large number of methods and for arbitrary body geometry. Reprints. (edc)