Applied PDE Group
Nonlinear Partial Differential Equations in Fluid and Solid Mechanics

DutKatMits2

Finite volume schemes for dispersive wave propagation and runup

D. Dutykh, Th. Katsaounis, D. Mitsotakis, Finite volume schemes for dispersive wave propagation and runupJournal of Computational Physics(JCP),  230(8):3035-3061, 2011​​​​
D. Dutykh, Th. Katsaounis, D. Mitsotakis
Finite volume method, Dispersive waves, Solitary waves, Runup, Water waves
2011
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.