A numerical study of variable depth KdV equations and generalizations of Camassa–Holm-like equations

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In this paper we numerically study the KdV-top equation and compare it with the Boussinesq equations over uneven bottoms. We use here a finite-difference scheme that conserves a discrete energy for the fully discrete scheme. We also compare this approach with the discontinuous Galerkin method. For the equations obtained in the case of stronger nonlinearities and related to the Camassa–Holm equation, we find several finite difference schemes that conserve a discrete energy for the fully discrete scheme. Because of its accuracy for the conservation of energy, our numerical scheme is also of interest even in the simple case of flat bottoms. We compare this approach with the discontinuous Galerkin method.

论文关键词:KdV equation,Camassa–Holm equation,Boussinesq system,Topography effect,Finite difference,Local discontinuous Galerkin

论文评审过程:Received 6 November 2011, Revised 4 April 2012, Available online 22 May 2012.

论文官网地址:https://doi.org/10.1016/j.cam.2012.05.010