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A 1D Stabilized Finite Element Model for Non-hydrostatic Wave Breaking and Run-up

  • P. Bacigaluppi
  • M. Ricchiuto
  • P. Bonneton
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 78)

Abstract

We present a stabilized finite element model for wave propagation, breaking and run-up. Propagation is modelled by a form of the enhanced Boussinesq equations, while energy transformation in breaking regions is captured by reverting to the shallow water equations and allowing waves to locally converge into discontinuities. To discretize the system we propose a non-linear variant of the stabilized finite element method of (Ricchiuto and Filippini, J.Comput.Phys. 2014). To guarantee monotone shock capturing, a non-linear mass-lumping procedure is proposed which locally reverts the third order finite element scheme to the first order upwind scheme. We present different definitions of the breaking criterion, including a local implementation of the convective criterion of (Bjørkavåg and Kalisch, Phys.Letters A 2011), and discuss in some detail the implementation of the shock capturing technique. The robustness of the scheme and the behaviour of different breaking criteria is investigated on several cases with available experimental data.

Keywords

Wave Height Wave Breaking Shallow Water Equation Boussinesq Equation Free Surface Velocity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Inria Bordeaux Sud-OuestTalence CedexFrance
  2. 2.UMR CNRS EPOCBordeaux UniversityTalenceFrance

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