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A robust, finite element model for hydrostatic surface water flows

Communications in Numerical Methods in Engineering

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DOI: 10.1002/(SICI)1099-0887(1998100)14:10<931::AID-CNM199>3.0.CO;2-X

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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
First page:
931
Last page:
940
Number of Pages:
10