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Wavelet‐based adaptive grids as applied to hydrodynamics
Author(s) -
Smith C. W.,
Zang J.,
Eatock Taylor R.
Publication year - 2007
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1657
Subject(s) - discretization , grid , finite volume method , wavelet , shallow water equations , context (archaeology) , stability (learning theory) , euler equations , mathematics , scheme (mathematics) , regular grid , euler's formula , computer science , mathematical analysis , geometry , mechanics , geology , physics , artificial intelligence , paleontology , machine learning
An adaptive, wavelet‐based, multiscale finite‐volume scheme is developed and employed to investigate applications in the simulation of water waves. Firstly, two one‐dimensional, strictly hyperbolic cases are investigated: shallow water and Euler equations. These are followed by two investigations using a finite‐volume formulation of Madsen and Sørensen's Boussinesq equations. Converged results were obtained in all cases, which demonstrate that the adaptive grid scheme is significantly faster than that on a uniform grid. In some cases, one‐seventh of the number of cells is required to obtain the same accuracy as that of the uniform grid. Issues of stability are discussed in the context of the particular problems modelled here with the Boussinesq equations, related to discretization of the high‐order spatial derivatives on a non‐uniform grid. Copyright © 2007 John Wiley & Sons, Ltd.