Dispersive wave runup on non-uniform shores
  Historically the finite volume methods have been developed for the numerical integration of conservation laws. In this study we present some recent results on the application of such schemes to dispersive PDEs. Namely, we solve numerically a representative of Boussinesq type equations in view of important applications to the coastal hydrodynamics. Numerical results of the runup of a moderate wave onto a non-uniform beach are presented along with great lines of the employed numerical method (see D. Dutykh et al. (2011) for more details). 
Denys Dutykh (LAMA), Theodoros Katsaounis, Dimitrios Mitsotakis (IMA)
physics.class-ph math.NA physics.ao-ph physics.comp-ph physics.flu-dyn