Author(s): Jack Bokaris; Kostas Anastasiou
Keywords: Amplitude dispersion; bottom friction; celerity distortion; finite volume method; friction coefficient; implicit time integration; mild-slope equation; Roe's flux function
Abstract: The processes of non-linear celerity distortion due to amplitude dispersion and energy dissipation due to bottom friction, whose effects are intensified in shallow waters, are incorporated into a finite volume solver of the mild-slope equation. Amplitude dispersion is taken into account in an iterative manner. The local energy dissipation due to bottom friction is computed using an existing model with appropriate expressions for the friction coefficient. Solutions to wave propagation problems are obtained on unstructured triangular meshes. Roe's flux function is used to evaluate the numerical fluxes at the triangular cell edges, and the conserved variables are updated implicitly in time. The incorporation of non-linear amplitude dispersion is found to improve significantly the agreement of computed results with laboratory data in non-linear wave propagation problems, while the effects of bottom friction are of secondary importance.