Numerical solution of the ‘classical’ Boussinesq system

D.C. Antonopoulos and V.A. Dougalis

Mathematics and Computers in Simulation (MATCOM), 2012, vol. 82, issue 6, 984-1007

Abstract: We consider the ‘classical’ Boussinesq system of water wave theory, which belongs to the class of Boussinesq systems modelling two-way propagation of long waves of small amplitude on the surface of water in a horizontal channel. (We also consider its completely symmetric analog.) We discretize the initial-boundary-value problem for these systems, corresponding to homogeneous Dirichlet boundary conditions on the velocity variable at the endpoints of a finite interval, using fully discrete Galerkin-finite element methods of high accuracy. We use the numerical schemes as exploratory tools to study the propagation and interactions of solitary-wave solutions of these systems, as well as other properties of their solutions.

Keywords: Water waves; ‘Classical’ Boussinesq systems; Initial-boundary-value problems; Fully discrete Galerkin-finite element methods; Solitary waves (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:82:y:2012:i:6:p:984-1007

DOI: 10.1016/j.matcom.2011.09.006

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