Revista de Matemática Aplicada e Computacional

Modeling Interactions and Shoaling of Solitary Waves Using a Hybrid Finite Volume and Finite Difference Solver

Abstract

Keh-Han Wang and Burak Turan

This paper presents a mixed finite volume and finite difference solver with results showing the solitary wave interactions and shoaling process by solving a set of conservative forms of Boussinesq equations. A second order accurate finite volume scheme is applied to the conservative terms of the governing equations while up to the second order finite difference formulations are used to discretize the dispersive source terms with higher order derivatives. The limiters and surface gradient method are implemented in the model to remove the unwanted spurious oscillations and preserve the still water condition without introducing errors at the interfaces. The performance of the present numerical solver is tested with results of head on collisions and shoaling of solitary waves compared against those from finite element models that were developed based on fully nonlinear weakly dispersive and weakly nonlinear weakly dispersive forms of the Boussinesq equations as well as analytical solutions and experimental observations.