A cubic‐spline boundary integral method for two‐dimensional free‐surface flow problems

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.

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