Hemming Andreas Schäffer


The convolution-type approach to deterministic wave modeling is briefly reviewed including both continuous and discrete formulations for the case of linear waves in one horizontal dimension (1DH). The associated discrete dispersion relation is presented and shown to accurately predict results of numerical simulations. This provides a tool for global error control and it is suggested that a similar approach is adopted for other deterministic wave models preferably along with a procedure for minimizing computational times while adhering to specified error tolerances. The discretization scheme for the 1DH convolution uses direct impulse-response-function sampling on a staggered grid. The explanation for the high accuracy of this approach is established and it is shown that the advantage does not carry over to the case of 2DH. This calls for an entirely different method and it is sketched how a weighted least squares technique in wavenumber space might provide a satisfactory alternative in 2DH. For variable depth this approach involves a slight distortion of physical space in order to retain a wavenumber-space formulation that resembles that of constant depth.


waves; wave transformation; convolution; non-uniform discrete Fourier transform; weighted least squares; discrete dispersion relation; error control

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