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AN ENTROPY VARIABLE FORMULATION AND APPLICATIONS FOR THE TWO-DIMENSIONAL SHALLOW WATER EQUATIONS

โœ Scribed by S. W. BOVA; G. F. CAREY

Publisher
John Wiley and Sons
Year
1996
Tongue
English
Weight
1015 KB
Volume
23
Category
Article
ISSN
0271-2091

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โœฆ Synopsis

A new symmetric formulation of the two-dimensional shallow water equations and a streamline upwind Petrov-Galerkm (SUPG) scheme are developed and tested. The symmetric formulation is constructed by means of a transformation of dependent variables derived fkom the relation for the total energy of the water column. This symmetric form is well suited to the SUPG approach as seen in analogous treatments of gas dynamics problems based on entropy variables. Particulars related to the construction of the upwind test functions and an appropriate discontinuity-capturing operator are included. A formal extension to the viscous, dissipative problem and a stability analysis are also presented. Numerical results for shallow water flow in a channel with (a) a step transition, (b) a curved wall transition and (c) a straight wall transition are compared with experimental and other computational results from the literature.

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