{"title":"Numerical Modeling of Wave Run-Up in Shallow Water Flows Using Moving Wet\/Dry Interfaces","authors":"Alia Alghosoun, Michael Herty, Mohammed Seaid","volume":130,"journal":"International Journal of Mechanical and Mechatronics Engineering","pagesStart":1757,"pagesEnd":1762,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10009331","abstract":"We present a new class of numerical techniques to
\r\nsolve shallow water flows over dry areas including run-up. Many
\r\nrecent investigations on wave run-up in coastal areas are based on
\r\nthe well-known shallow water equations. Numerical simulations have
\r\nalso performed to understand the effects of several factors on tsunami
\r\nwave impact and run-up in the presence of coastal areas. In all these
\r\nsimulations the shallow water equations are solved in entire domain
\r\nincluding dry areas and special treatments are used for numerical
\r\nsolution of singularities at these dry regions. In the present study we
\r\npropose a new method to deal with these difficulties by reformulating
\r\nthe shallow water equations into a new system to be solved only in the
\r\nwetted domain. The system is obtained by a change in the coordinates
\r\nleading to a set of equations in a moving domain for which the
\r\nwet\/dry interface is the reconstructed using the wave speed. To solve
\r\nthe new system we present a finite volume method of Lax-Friedrich
\r\ntype along with a modified method of characteristics. The method is
\r\nwell-balanced and accurately resolves dam-break problems over dry
\r\nareas.","references":"[1] D. Zhi and Z. Jie-min. Numerical modeling of wave evolution and\r\nRun up in shallow water. Journal of hydrodynamics. 2009,21(6), pp. 731\r\n- 738.\r\n[2] S. Bi, J. Zhou, Y. Liu and L. Song. A finite volume method for\r\nmodeling shallow flows with wet-dry fronts on Adaptive cartesian grids.\r\nMathematical problems in Engineering. 2014, pp. 20.\r\n[3] Y. Peng, J. Zhou, and R. Burrows, Modelling solute transport in shallow\r\nwater with Lattice Boltzmann method. Computer and Fluids . 2011(50),\r\npp. 181-188.\r\n[4] L. Yinerg, and P. Huang, A coupled Lattice Boltzmann model for\r\nadvection and anistropic dispersion problem in shallow water. Advances\r\nin water Resources. 208(31), pp. 1719-1730.\r\n[5] H. Johnson, and J. Zyserman. Controlling Spatial Oscillations in bed level\r\nupdate schemes. Coastal engineering, 2016(46).\r\n[6] T. Pongsuansin, M. Maleewong and K. Meckchay. Consistent weighted\r\naverage flux of well - Balanced TVD - RK Discontinuous Galerkin Method\r\nfor shallow water flows. Modelling and simulation in Engineering, 2015,\r\npp. 1-11.\r\n[7] R. Ata, S. Pavan, S. Khellade and E. Toro. A weighted average flux (WAF)\r\nscheme applied to shallow water equations for real life applications.\r\nAdvances in water Resources, 2013(62), pp. 115 - 172.\r\n[8] X. Lin, A.Mohammadian, and J. Sedano. A well - balanced 2-D model for\r\nDam-Break flow with wetting and drying . Proceedins of the international\r\nconference on new trends in transport phenomena. Ottawa, Ontario, 2014,\r\npp. (55).\r\n[9] O. Lglesias, G.Lastras, C.Souto, S.Costa and M. Canals. Effects of\r\ncoastal submarine canyons on tsunami propagation and impact.Marine\r\nGeology, 2014(350), pp.39 - 51.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 130, 2017"}