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Shoreline tracking and implicit source terms for a well balanced inundation model. (English) Zbl 1425.86004
Summary: The HyFlux2 model has been developed to simulate severe inundation scenario due to dam break, flash flood and tsunami-wave run-up. The model solves the conservative form of the two-dimensional shallow water equations using the finite volume method. The interface flux is computed by a Flux Vector Splitting method for shallow water equations based on a Godunov-type approach. A second-order scheme is applied to the water surface level and velocity, providing results with high accuracy and assuring the balance between fluxes and sources also for complex bathymetry and topography. Physical models are included to deal with bottom steps and shorelines. The second-order scheme together with the shoreline-tracking method and the implicit source term treatment makes the model well balanced in respect to mass and momentum conservation laws, providing reliable and robust results.
The developed model is validated in this paper with a 2D numerical test case and with the Okushiri tsunami run up problem. It is shown that the HyFlux2 model is able to model inundation problems, with a satisfactory prediction of the major flow characteristics such as water depth, water velocity, flood extent, and flood-wave arrival time. The results provided by the model are of great importance for the risk assessment and management.
MSC:
86A05 Hydrology, hydrography, oceanography
35Q35 PDEs in connection with fluid mechanics
76M12 Finite volume methods applied to problems in fluid mechanics
Software:
CLAWPACK; MOST
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References:
[1] Morris MW. CADAM concerted action on dambreak modelling. Final Report. Report SR 571, January 2000.
[2] Chanson, Tsunami surges on dry coastal plains: application of dam break wave equations, Coastal Engineering Journal 48 (4) pp 355– (2006)
[3] The NGDC Tsunami event database. Available from: http://www.ngdc.noaa.gov/seg/hazard/tsevsrch_idb.shtml.
[4] Titov VV, Gonzalez FI. Implementation and testing of the method of splitting tsunami (MOST) model. NOAA Technical Memorandum ERL PMEL-112, 1997.
[5] Shuto N, Imamura F, Yalciner AC. TUNAMI-N2 tsunami modelling manual. Available from: http://tunamin2.ce.metu.edu.tr/.
[6] Mader, Numerical Modelling of Water Waves (2004) · Zbl 1081.76001 · doi:10.1201/9780203492192
[7] LeVeque RJ. The CLAWPACK software package. Available from: http://www.amath.washington.edu/claw/.
[8] Brufau, Two-dimensional dam break flow simulation, International Journal for Numerical Methods in Fluids 33 (1) pp 35– (2000) · Zbl 0974.76535
[9] Brufau, Zero mass error using unsteady wetting-drying conditions in shallow flows over dry irregular topography, International Journal for Numerical Methods in Fluids 45 (10) pp 1047– (2004) · Zbl 1060.76584
[10] Liang, Simulation of dam- and dyke-break hydrodynamics on dynamically adaptive quadtree grids, International Journal for Numerical Methods in Fluids 46 (2) pp 127– (2004) · Zbl 1060.76590
[11] Guinot, Flux and source term discretization in two-dimensional shallow water models with porosity on unstructured grids, International Journal for Numerical Methods in Fluids 50 (3) pp 309– (2006) · Zbl 1086.76048
[12] Murillo, The influence of source terms on stability, accuracy and conservation in two-dimensional shallow flow simulation using triangular finite volumes, International Journal for Numerical Methods in Fluids 54 (5) pp 543– (2007) · Zbl 1204.76023
[13] European Commission, Joint Research Centre, Major Accident Hazards Bureau (MAHB). Available from: http://mahbsrv.jrc.it/.
[14] Natural and Environmental Disaster Information Exchange System (NEDIES). Available from: http://nedies.jrc.it.
[15] Krausmann, A qualitative Natech damage scale for the impact of floods on selected industrial facilities, Natural Hazards 46 (2) pp 179– (2008)
[16] Franchello G. Modelling shallow water flows by a High Resolution Riemann Solver. EUR 23307 EN-2008, 2008; ISSN: 1018-5593. Available from: http://bookshop.europa.eu/eubookshop/download.action?fileName=LBNA23307ENC_002.pdf&eubphfUid=627660&catalogNbr=LB-NA-23307-EN-C.
[17] Franchello G, Krausmann E. HyFlux2: a numerical model fort he impact assessment of severe inundation scenario to chemical facilities and downstream environment. EUR 23354 EN-2008, 2008; ISSN: 1018-5593E. Available from: http://bookshop.europa.eu/eubookshop/download.action?fileName=LBNA23354ENC_002.pdf&eubphfUid=628038&catalogNbr=LB-NA-23354-EN-C.
[18] Toro, Shock-capturing Methods for Free-surface Shallow Flows (2001) · Zbl 0996.76003
[19] Ruel F. Numerical simulation of reacting gas flows. Basic models and algorithms. Presentation of a preliminary code version. JRC Technical Note No. I.91.109, 1991.
[20] Städtke H, Franchello G, Worth B. Numerical simulation of multi-dimensional two-phase flow using second order flux splitting technique’s. Seventh International Meeting on Nuclear Thermal Hydraulics, NURETH-7, Saratoga Springs, NY, U.S.A., 1995.
[21] Städtke, Gasdynamic Aspects of Two-phase Flow. Hyperbolicity, Wave Propagation Phenomena, and Related Numerical Methods (2006) · doi:10.1002/9783527610242
[22] Audusse, A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water ows, SIAM Journal on Scientific Computing 25 (6) pp 2050– (2004) · Zbl 1133.65308
[23] Marche F. Theoretical and numerical study of shallow water models. Applications to nearshore hydrodynamics. Thesis Université de Bordeaux. Available from: http://www.math.u-bordeaux.fr/marche/THESE_Marche.pdf.
[24] Brufau, Unsteady free surface flow simulation over complex topography with a multidimensional upwind technique, Journal of Computational Physics 186 (2) pp 503– (2003) · Zbl 1047.76537
[25] Delis, A robust high-resolution finite volume scheme for the simulation of long waves over complex domains, SO: International Journal for Numerical Methods in Fluids 56 (4) pp 419– (2008) · Zbl 1129.76031
[26] George, Finite volume methods and adaptive refinement for global tsunami propagation and local inundation, Science of Tsunami Hazards 24 (5) pp 319– (2006)
[27] The Third International Workshop on Long-wave Runup Models, Wrigley Marine Science Center, Catalina Island, CA, 17-18 June 2004. Available from: http://www.cee.cornell.edu/longwave/.
[28] Matsuyama M, Tanaka H. An experimental study of the highest run-up height in the 1993 Hokkaido Nansei-oki earthquake tsunami. ITS 2001 Proceeding, session 7, 7-21 Number 2001. Available from: http://nthmp-history.pmel.noaa.gov/its2001/Separate_Papers/7-21_Matsuyama.pdf.
[29] Yeh H. Tsunami loading on structure. Paper presented at the International Workshop on Fundamentals of Coastal Effects of Tsunamis, Hilo, Hawaii, 26-28 December 2006. Available from: http://tsunami.orst.edu/workshop/2006/agenda.html.
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