# 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. |