Finite volume schemes for dispersive wave propagation and runup

Abstract

Finite volume schemes are commonly used to construct approximate solutions to conservation laws. In this study we extend the framework of the finite volume methods to dispersive water wave models, in particular to Boussinesq type systems. We focus mainly on the application of the method to bidirectional nonlinear, dispersive wave propagation in one space dimension. Special emphasis is given to important nonlinear phenomena such as solitary waves interactions, dispersive shock wave formation and the runup of breaking and non-breaking long waves.

Keywords

Bibliographic record

BibTeX Citation

@article{Dutykh2011finitevolume,
  author = {Dutykh, D. and Katsaounis, Th. and Mitsotakis, D.},
  title = {Finite volume schemes for dispersive wave propagation and runup},
  journal = {J. Comp. Phys.},
  year = {2011},
  volume = {230},
  pages = {3035--3061},
  doi = {10.1016/j.jcp.2011.01.003},
  abstract = {Finite volume schemes are commonly used to construct approximate solutions to conservation laws. In this study we extend the framework of the finite volume methods to dispersive water wave models, in particular to Boussinesq type systems. We focus mainly on the application of the method to bidirectional nonlinear, dispersive wave propagation in one space dimension. Special emphasis is given to important nonlinear phenomena such as solitary waves interactions, dispersive shock wave formation and the runup of breaking and non-breaking long waves.},
  keywords = {math.AP, math.NA, physics.class-ph, physics.comp-ph, physics.ao-ph, Mathematics, Physics, physics.flu-dyn}
}