A robust, finite element model for hydrostatic surface water flows

Communications in Numerical Methods in Engineering
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Abstract

A finite element scheme is introduced for the 2-dimensional shallow water equations using semi-implicit methods in time. A semi-Lagrangian method is used to approximate the effects of advection. A wave equation is formed at the discrete level such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. The convergence rates and relative computational efficiency are examined with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids.A finite element scheme is introduced for the 2-dimensional shallow water equations using semi-implicit methods in time. A semi-Lagrangian method is used to approximate the effects of advection. A wave equation is formed at the discrete level such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. The convergence rates and relative computational efficiency are examined with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids.

Additional publication details

Publication type Article
Publication Subtype Journal Article
Title A robust, finite element model for hydrostatic surface water flows
Series title Communications in Numerical Methods in Engineering
DOI 10.1002/(SICI)1099-0887(1998100)14:10<931::AID-CNM199>3.0.CO;2-X
Volume 14
Issue 10
Year Published 1998
Language English
Publisher John Wiley & Sons Ltd
Publisher location Chichester, United Kingdom
Larger Work Type Article
Larger Work Subtype Journal Article
Larger Work Title Communications in Numerical Methods in Engineering
First page 931
Last page 940