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Original Articles

A Numerical Model for Storm Surges that Involve the Inundation of Complex Landscapes

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Pages 1550017-1-1550017-30 | Received 28 Apr 2015, Accepted 13 Aug 2015, Published online: 10 Jan 2018

References

  • Bermudez, A. & Vazquez, M. E. [1994] “Upwind methods for hyperbolic conservation laws with source terms,” Computers Fluids 23 (8), 1049–1071.
  • Bunya, S. , Dietrich, J. C. , Westerink, J. J. , Ebersole, B. A. , Smith, J. H. , Atkinson, J. H. , Jensen, R. , Resio, D. T. , Luettich, R. A. , Dawson, C. , Cardone, V. J. , Cox, A. T. , Powell, M. D. , Westerink, H. J. & Roberts, H. J. [2012] “A high-resolution coupled riverine flow, tide, wind, wind wave, and storm surge model for southern Louisiana and Mississippi. Part I: Model development and validation,” Mon. Weather Rev. 138, 345–377.
  • Carrier, G. F. & Greenspan, H. P. [1958] “Water waves of finite amplitude on a sloping beach,” J. Fluid Mech. 4, 97–109.
  • Castro, J. M. , Ferreiro, A. M. , Garcia-Rodriguez, J. A. , Gonzalez-Vida, J. M. , Macias, J. , Pares, C. & Vasquez-Cendon, M. E. [2005] “The numerical treatment of wet/dry fronts in shallow-water flows: Application to one-layer and two-layer systems,” Math. Comput. Modell. 42 (255), 419–426.
  • Casulli, V. & Walters, R. A. [2000] “An unstructured, three-dimensional model based on the shallow water equations,” Int. J. Numer. Methods Fluids 32, 331–348.
  • Chen, C. , Liu, H. & Beardsley, R. C. [2003] “An unstructured grid, finite-volume, three-dimensional, primitive equations ocean model: Application to coastal ocean and estuaries,” J. Atmos. Oceanic Technol. 20, 159–186.
  • Coirier, W. J. & Powell, K. G. [1996] “Solution-adaptive Cartesian cell approach for viscous and inviscid flows,” AIAA J. 34, 938–945.
  • Davis, J. R. & Sheng, Y. P. [2003] “Development of a parallel storm surge model,” Int. J. Numer. Methods Fluids 42, 549–580.
  • De Zeeuw, D. & Powell, K. G. [1993] “An adaptively refined Cartesian mesh solver for the Euler equations,” J. Comput. Phys. 104, 56–68.
  • Dumbser, M. & Toro, E. F. [2011] “A simple extension of the Osher Riemann solver to non-conservative hyperbolic systems,” J. Sci. Computing 48, 70–88.
  • Erduran, K. S. , Kutija, V. & Hewett, C. J. M. [2002] “Performance of finite volume solutions to the shallow water equations with shock-capturing schemes,” Int. J. Numer. Methods Fluids 40, 1237–1273.
  • Ferreira, C. M. , Olivera, F. & Irish, J. L. [2014] “ARC stormsurge: Integrating hurricane storm surge modeling and GIS,” J. Am. Water Resources Assoc. 50, 219–233.
  • Forbes, C. , Fleming, J. G. , Mattocks, C. , Fulcher, C. W. , Luettich, R. A. , Westerink, H. J. & Bunya, S. [2007] “New developments in the ADCIRC community model,” in Proc. 10th Int. Conf. Estuarine and Coastal Modeling (A.S.C.E., Newport, RI), pp. 373–392.
  • Freeman, J. C. , Bear, L. & Hung, C. H. [1957] “The bathystrophic storm tide,” J. Marine Res. 16, 12–23.
  • Greaves, D. & Borthwick, A. [1999] “Hierarchical tree-based nite element mesh generation,” Int. J. Numer. Methods Eng. 41, 447–471.
  • Hirsch, C. [1990] Numerical Computation of Internal and External Flows (Wiley, New York).
  • Holland, G. J. [1980] “An analytic model of the wind and pressure profiles in hurricanes,” Monthly Weather Rev. 108, 1212–1218.
  • Jelesnianski, C. P. , Chen, J. & Shaffer, W. [1992] “SLOSH: Sea, lake, and overland surges from hurricane,” Technical Report, National Weather Service.
  • Jin, S. [2001] “A steady-state capturing method for hyperbolic systems with geometrical source terms,” Math. Modelling Numer. Anal. 35, 631–645.
  • Johns, B. [1982] “Numerical integration of the shallow water equations over a sloping shelf,” Int. J. Numer. Methods Fluids 2, 253–261.
  • Kelly, D. M. [2015] “On the treatment of geometric source terms when using Osher's approximate Riemann solver for the shallow water equations,” Working Paper 101: Extreme Events Institute, International Hurricane Research Center, Florida International University.
  • Large, W. G. & Pond, S. [1981] “Open ocean momentum fluxes in moderate to strong winds,” J. Phys. Oceanography 11, 324–336.
  • Liang, Q. [2010] “Flood simulation using a well-balanced shallow flow model,” J. Hydraulic Eng. 136, 669–675.
  • Liang, Q. & Borthwick, A. G. L. [2009] “Adaptive quadtree simulation of shallow flows with wet-dry fronts over complex topography,” Computers Fluids 38, 221–234.
  • Liang, Q. , Borthwick, A. G. L. & Stelling, G. [2004] “Simulation of dam- and dyke-break hydrodynamics on dynamically adaptive quadtree grids,” Int. J. Numer. Methods Fluids 46, 127–162.
  • Liang, Q. & Marche, F. [2009] “Numerical resolution of well-balanced shallow water equations with complex source terms,” Adv. Water Res. 32, 873–884.
  • Liang, Q. , Zang, J. , Borthwick, A. G. L. & Taylor, P. H. [2007] “Shallow flow simulation on dynamically adaptive cut cell quadtree grids,” Int. J. Numer. Methods Fluids 53, 1777–1799.
  • Morey, S. L. , Baig, S. , Bourassa, M. A. , Dukhovskoy, D. S. & OBrien, J. J. [2006] “Remote forcing contribution to storm-induced sea level rise during hurricane Dennis,” Geophys. Res. Lett. 33, doi: 10.1029/2006GL027021.
  • Mungkasi, S. k. Roberts, S. G. [2012] “Approximation of the carrier Greenspan periodic solution to the shallow water wave equations for flows on a sloping beach,” Int. J. Numer. Methods Fluids 69, 763–780.
  • Ning, L. , Emanuel, K. , Openheimer, M. & Vanmarcke, E. [2012] “Physically based assessment of hurricane surge threat under climate change,” Nat. Clim. Change 2 (6), 462–467.
  • NOAA [2009] National Hurricane center storm surge overview, Available at http://www.nhc.noaa.gov/surge/.
  • Osher, S. & Solomon, F. [1982] “Upwind difference schemes for hyperbolic systems of conservation laws,” Math. Comput. 38, 339–374.
  • Park, K. & Borthwick, A. G. L. [2001] “Quadtree grid numerical model of nearshore wave-current interaction,” J. Coastal Eng. 42, 219–239.
  • Popinet, S. [2012] “Adaptive modelling of long-distance wave propagation and fine-scale flooding during the Tohoku tsunami,” Nat. Hazards Earth Syst. Sci. 12 (4), 1213–1227.
  • Pu, J. H. , Nian-Sheng Cheng, N.-S. , Tan, S. T. & Shao, S. [2012] “Source term treatment of SWEs using surface gradient upwind method,” J. Hydraulic Res. 50 (2), 145–153.
  • Rego, J. L. & Li, C. [2008] “On the importance of the forward speed of hurricanes in storm surge forecasting: A numerical study,” Geophys. Res. Lett. 36, doi:10.1029/2008GL036953.
  • Rogers, B. , Fujihara, M. & Borthwick, A. G. L. [2001] “Adaptive Q-tree Godunov-type scheme for shallow water equations,” Int. J. Numer. Methods Fluids 35, 247–280.
  • Sampson, J. , Easton, A. & Singh, M. [2006] “Moving boundary shallow water flow above parabolic bottom topography,” Math. Comput. 47, C373–C378.
  • Spekreijse, S. P. [1987] “Multigrid solution of the steady Euler equations,” PhD Thesis, Centre for Mathematics and Computer Science Amsterdam.
  • Strang, G. [1968] “On the construction and comparison of difference schemes,” SIAM J. Numer. Anal. 124, 506–517.
  • Svard, M. , Gong, J. & Nordstrom, J. [2008] “An accuracy evaluation of unstructured node—centered finite-volume methods,” Appl. Numer. Math. 58, 1142–1158.
  • Thacker, W. [1981] “Some exact solutions to the non-linear shallow water wave equations,” J. Fluid Mech. 107, 499–508.
  • Toro, E. F. [1997] Riemann Solvers and Numerical Methods for Fluid Dynamics (Springer, Berlin).
  • Toro, E. F. [2001] Shock-Capturing Methods for Free-Surface Shallow Flows (Wiley, New York, NY).
  • Westerink, J. J. , Luettich, R. A. , Feyen, J. C. , Atkinson, J. H. , Dawson, C. , Roberts, H. J. , Powell, M. D. , Dunion, J. P. , Kubatko, E. J. & Pourtaheri, H. [2008] “A basin- to channel-scale unstructured grid hurricane storm surge model applied to southern Louisiana,” Mon. Weather Rev. 136, 833–864.
  • Xie, L. , Pietrafesa, L. J. & Peng, M. [2004] “Incorporation of a mass-conserving inundation scheme into a three dimensional storm surge model,” J. Coastal Res. 20, 1209–1223.
  • Zhang, K. , Xiao, C. & Shen, J. [2008] “Comparison of the CEST and SLOSH models for storm surge flooding,” J. Coastal Res. 24, 489–499.
  • Zhang, K. , Xiao, C. & Shen, J. [2013] “Transition of the coastal and Estuarine storm tide model to an operational forecast model: A case study of Florida,” Weather Forecasting 28, 1019–1037.
  • Zhang, Y. & Baptista, A. M. [2008] “SELFE: A semi-implicit Eulerian—Lagrangian finite-element model for cross-scale ocean circulation,” Ocean Modell. 21, 71–96.
  • Zhao, D. H. , Shen, H. W. , Lai, J. S. & Tabios III, G. Q. [1996] “Approximate Riemann solvers in FVM for 2D hydraulic shock wave modeling,” J. Hydraulic. Eng. (ASCE) 122 (12), 692–702.

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