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A cascadic conjugate gradient algorithm for mass conservative, semi‐implicit discretization of the shallow water equations on locally refined structured grids
Author(s) -
Bonaventura Luca,
Rosatti Giorgio
Publication year - 2002
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.274
Subject(s) - discretization , conjugate gradient method , mathematics , shallow water equations , diagonal , diagonally dominant matrix , cartesian coordinate system , grid , conservation of mass , helmholtz equation , geometry , mathematical analysis , algorithm , mechanics , physics , pure mathematics , boundary value problem , invertible matrix
A semi‐implicit, mass conservative discretization scheme is applied to the two‐dimensional shallow water equations on a hierarchy of structured, locally refined Cartesian grids. Different resolution grids are fully interacting and the discrete Helmholtz equation obtained from the semi‐implicit discretization is solved by the cascadic conjugate gradient method. A flux correction is applied at the interface between the coarser and finer discretization grids, so as to ensure discrete mass conservation, along with symmetry and diagonal dominance of the resulting matrix. Two‐dimensional idealized simulations are presented, showing the accuracy and the efficiency of the resulting method. Copyright © 2002 John Wiley & Sons, Ltd.