Shoreline tracking and implicit source terms for a well balanced inundation model.

*(English)*Zbl 1425.86004Summary: 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.

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 |

##### Keywords:

2D shallow water equations; Riemann Solver; Flux Vector Splitting; implicit source terms; complex topography; shoreline tracking; dam break; tsunami run-up; impact assessment
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\textit{G. Franchello}, Int. J. Numer. Methods Fluids 63, No. 10, 1123--1146 (2010; Zbl 1425.86004)

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