RECENT EXTENSIONS TO LOCAL POLYNOMIAL APPROXIMATION MODELS

Andrew B. Kennedy

Abstract


Local polynomial approximation models for water wave simulation are examined with the aim of improving accuracy and efficiency. Several potential improvements are considered. The first is based on a linearisation of the solution for Laplace's equation and is shown to have good theoretical characteristics. However, it is found to have a fatal instability to high wavenumber bottom disturbances. The second method uses empirical collocation adjustment to provide better agreement with exact solutions for steady waves. This method provides significant improvements in accuracy for a given level of approximation and is recommended for future use.

Keywords


polynomial approximation; model extension

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