Optimal Parameter Selection in GWC-based Shallow ...

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XVI International Conference on Computational Methods in Water Resources (CMWR-XVI) Ingeniørhuset

Optimal Parameter Selection in GWC-based Shallow Water Models
Author:Evan Tromble <etromble@ou.edu> (University of Oklahoma)
Randall Kolar <kolar@ou.edu> (University of Oklahoma)
Presenter:Evan Tromble <etromble@ou.edu> (University of Oklahoma)
Date: 2006-06-18     Track: General Sessions     Session: General
DOI:10.4122/1.1000000380

One strategy for solving the shallow water equations in the finite element community is to reformulate the primitive continuity equation into the generalized wave continuity equation (GWCE). The GWCE contains a parameter, “G,” as well as the second derivatives in space and time that are generally associated with the classic wave equation (hence its name). G is a numerical parameter: as G goes to zero, the equation reduces to the form of a pure wave equation, and as G goes to infinity, the equation takes the form of the primitive continuity equation. Atkinson et al. [1] found that the GWCE formulation is equivalent to the quasi-bubble discretization (as applied to the linearized shallow water equations) for a specific value of G, which depends on the wave frequency and the bottom friction parameter. Additionally, they theorize that this relationship for G which makes them equivalent also yields optimal dispersion properties. Numerical simulations using such a space and time-variable G parameter based on the quasi-bubble/GWCE comparison have yielded favorable initial results: the variable G implementation substantially reduces wave constituent and mass balance errors for highly non-linear cases. In particular, for a 1-D linear sloping beach with wetting and drying and an M2 forcing, the error with the variable G is two orders of magnitude less for the steady and M2 constituents than with a constant G. The M4 and M6 constituent errors are an order of magnitude less and the mass balance errors decrease by 20%. Due to such promising results from the 1-D study, the variable G formulation is being implemented in a 2-D depth-averaged production code; simulations will be run on a variety of idealized and real basins and selected results will be presented. [1] J.H. Atkinson, J.J. Westerink, and J.M. Hervouet. Similarities between the Quasi-Bubbl and the Generalized Wave Continuity Equation solutions to the Shallow Water Equations. International Journal for Numerical Methods in Fluids, 45, 2004; 689-714.