Well-Balanced Finite-Volume Model for Long-Wave Runup
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 132, Issue 2
Abstract
This paper presents a two-dimensional, well-balanced finite-volume model for runup of long waves under nonbreaking and breaking conditions. The model uses a conservative form of the nonlinear shallow-water equations with source terms and an explicit Godunov-type scheme along with the exact Riemann solver for the flux and moving waterline. A second-order scheme splits the two-dimensional problem into two sequential one-dimensional problems for time integration. The surface-gradient method leads to a well-balanced formulation of the flux and source terms and a piecewise linear interpolation reconstructs numerical data at cell interfaces to achieve second-order accuracy in space. This provides accurate descriptions of the conserved variables and small flow-depth perturbations near the moving waterline. The computed surface elevation, flow velocity, and runup show very good agreement with previous asymptotic and analytical solutions as well as laboratory data. The model accurately describes breaking waves as bores or hydraulic jumps and conserves volume across flow discontinuities.
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Acknowledgments
This publication was funded in part by a grant/cooperative agreement from the National Oceanic and Atmospheric Administration (NOAA), Project No. R/EP-20, which is sponsored by the University of Hawaii Sea Grant College Program, School of Ocean and Earth Science and Technology (SOEST), under Institutional Grant No. NA16RG2254 from NOAA Office of Sea Grant, Department of Commerce. Additional support was provided by the National Tsunami Hazard Mitigation Program via Hawaii State Civil Defense for the Hawaii Tsunami Mapping Project as well as the Office of Naval Research via Grant No. N00014-02-1-0903 for the ENDEAVOR project. The writers would like to thank Dr. Michael J. Briggs for providing the conical island test data as well as the Associate Editor and three anonymous reviewers for their thorough reviews and constructive remarks. The views expressed herein are those of the writers and do not necessarily reflect the views of NOAA and any of its sub-agencies. UNIHI-SEAGRANT-JC-05-03. SOEST Contribution No. 6600.
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Information
Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 132 • Issue 2 • March 2006
Pages: 114 - 124
Copyright
© 2006 ASCE.
History
Received: Jun 2, 2004
Accepted: May 16, 2005
Published online: Mar 1, 2006
Published in print: Mar 2006
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