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Numerical analysis of time‐dependent Boussinesq models
Author(s) -
van der Houwen P. J.,
Mooiman J.,
Wubs F. W.
Publication year - 1991
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.1650131004
Subject(s) - boussinesq approximation (buoyancy) , discretization , mathematics , shallow water equations , integrator , runge–kutta methods , stability (learning theory) , mathematical analysis , numerical analysis , mechanics , physics , computer science , convection , natural convection , quantum mechanics , voltage , machine learning , rayleigh number
In this paper we analyse numerical models for time‐dependent Boussinesq equations. These equations arise when so‐called Boussinesq terms are introduced into the shallow water equations. We use the Boussinesq terms proposed by Katapodes and Dingemans. These terms generalize the constant depth terms given by Broer. The shallow water equations are discretized by using fourth‐order finite difference formulae for the space derivatives and a fourth‐order explicit time integrator. The effect on the stability and accuracy of various discrete Boussinesq terms is investigated. Numerical experiments are presented in the case of a fourth‐order Runge‐Kutta time integrator.