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A cubic‐spline boundary integral method for two‐dimensional free‐surface flow problems
Author(s) -
Sen Debabrata
Publication year - 1995
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620381103
Subject(s) - free surface , mathematics , velocity potential , boundary element method , mathematical analysis , potential flow , computation , surface (topology) , spline (mechanical) , boundary value problem , constant (computer programming) , geometry , finite element method , algorithm , mechanics , computer science , physics , structural engineering , engineering , programming language
Abstract A cubic‐spline boundary‐integral‐equation method is presented for solution of free‐surface potential problems in two dimensions. In this scheme, it is possible to enforce a condition of conitnuous velocity through a geometric corner point in addition to the condition of continuous potential. Only the latter condition is possible in a linear‐element version of the model. A detailed description of the method is provided. Test computations concerning a propagating linear wave show a remarkable improvement in the performance of the method compared to the linear and constant‐element versions, both of which are prevalent in free‐surface hydrodynamics applications. What is particularly emphasized is the level of accuracy that can be achieved from the presented method both globally and locally at and near the corner.