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Numerical solution of the ‘classical’ Boussinesq system

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  • Antonopoulos, D.C.
  • Dougalis, V.A.

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.

Suggested Citation

  • Antonopoulos, D.C. & Dougalis, V.A., 2012. "Numerical solution of the ‘classical’ Boussinesq system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(6), pages 984-1007.
    • Handle: RePEc:eee:matcom:v:82:y:2012:i:6:p:984-1007
    DOI: 10.1016/j.matcom.2011.09.006
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    References listed on IDEAS

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    1. Pelloni, Beatrice & Dougalis, Vassilios A., 2001. "Numerical modelling of two-way propagation of non-linear dispersive waves," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 55(4), pages 595-606.
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