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


Dispersive wave runup on non-uniform shores

​D. Dutykh, Th. Katsaounis,  D. Mitsotakis, Dispersive wave runup on non-uniform shores, Finite volumes for complex application VI,€“ Problems & Perspectives. Springer Proceedings in Mathematics, vol. 4, pp. 389 - 397, 2011
D. Dutykh, Th. Katsaounis, D. Mitsotakis
finite volume schemes, Boussinesq equation, runup
​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) [7] for more details)