Similarities between the quasi-bubble and the generalized wave continuity equation solutions to the shallow water equations

✍ Scribed by J. H. Atkinson; J. J. Westerink; J. M. Hervouet

• Publisher: John Wiley and Sons
• Year: 2004
• Tongue: English
• Weight: 258 KB
• Volume: 45
• Category: Article
• ISSN: 0271-2091
• DOI: 10.1002/fld.700

✦ Synopsis

Abstract

Two common strategies for solving the shallow water equations in the finite element community are the generalized wave continuity equation (GWCE) reformulation and the quasi‐bubble velocity approximation. The GWCE approach has been widely analysed in the literature. In this work, the quasi‐bubble equations are analysed and comparisons are made between the quasi‐bubble approximation of the primitive form of the shallow water equations and a linear finite element approximation of the GWCE reformulation of the shallow water equations. The discrete condensed quasi‐bubble continuity equation is shown to be identical to a discrete wave equation for a specific GWCE weighting parameter value. The discrete momentum equations are slightly different due to the bubble function. In addition, the dispersion relationships are shown to be almost identical and numerical experiments confirm that the two schemes compute almost identical results. Analysis of the quasi‐bubble formulation suggests a relationship that may guide selection of the optimal GWCE weighting parameter. Copyright © 2004 John Wiley & Sons, Ltd.