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A method for analysing nesting techniques for the linearized shallow water equations
Author(s) -
Heggelund Yngve,
Berntsen Jarle
Publication year - 2001
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.215
Subject(s) - nesting (process) , eigenvalues and eigenvectors , spectral radius , shallow water equations , mathematics , stability (learning theory) , matrix (chemical analysis) , test case , grid , radius , waves and shallow water , mathematical analysis , geology , geometry , computer science , engineering , physics , statistics , materials science , mechanical engineering , regression analysis , computer security , quantum mechanics , oceanography , machine learning , composite material
A method for analysing different nesting techniques for the linearized shallow water equations is presented. The problem is formulated as an eigenvector–eigenvalue problem. A necessary condition for stability is that the spectral radius of the propagation matrix is less than or equal to one. Two test cases are presented. The first test case is analysed, and effects of enforcing volume conservation and nudging in time are studied. A nesting technique is found that causes no growth of any eigenvectors for reasonable time steps. This nesting technique is then used on both test cases, and results are compared to an everywhere refined model and a coarse grid model. Copyright © 2002 John Wiley & Sons, Ltd.