Second-order finite volume with hydrostatic reconstruction for tsunami simulation

Abstract

Tsunami modeling commonly accepts the shallow water system as governing equations where the major difficulty is the correct treatment of the nonconservative term due to bathymetry variations. The finite volume method for solving the shallow water equations with such source terms has received great attention in the two last decades. The built-in conservation property, the capacity to correctly treat discontinuities, and the ability to handle complex bathymetry configurations preserving some steady state configurations (well-balanced scheme) make the method very efficient. Nevertheless, it is still a challenge to build an efficient numerical scheme, with very few numerical artifacts (e.g., small numerical diffusion, correct propagation of the discontinuities, accuracy, and robustness), to be used in an operational environment, and that is able to better capture the dynamics of the wet-dry interface and the physical phenomena that occur in the inundation area. In the first part of this paper, we present a new second-order finite volume code. The code is developed for the shallow water equations with a nonconservative term based on the hydrostatic reconstruction technology to achieve a well-balanced scheme and an adequate dry/wet interface treatment. A detailed presentation of the numerical method is given. In the second part of the paper, we highlight the advantages of the new numerical technique. We benchmark the numerical code against analytical, experimental, and field results to assess the robustness and the accuracy of the numerical code. Finally, we use the 28 February 1969 North East Atlantic tsunami to check the performance of the code with real data.Historical data for Cascais and Lagos (1969 Lisbon Tsunami) are available at http://www.dgterritorio.pt/cartografia_e_geodesia/geodesia/redes_geodesicas/rede_maregrafica/. The tagus estuary data (typewriter document) are available at the Dom Luiz Institute library http://idl.ul.pt/node/33. This work is funded by the Portugal-France research agreement, through the research project GEONUM FCT-ANR/MAT-NAN/0122/2012. This research was financed by Portuguese Funds through FCT-Fundacao para a Ciencia e a Tecnologia, within the Project UID/MAT/00013/2013