Development of a Combined Compact Difference Scheme to Simulate Soliton Collision in a Shallow Water Equation
Year: 2016
Communications in Computational Physics, Vol. 19 (2016), Iss. 3 : pp. 603–631
Abstract
In this paper a three-step scheme is applied to solve the Camassa-Holm (CH) shallow water equation. The differential order of the CH equation has been reduced in order to facilitate development of numerical scheme in a comparatively smaller grid stencil. Here a three-point seventh-order spatially accurate upwinding combined compact difference (CCD) scheme is proposed to approximate the first-order derivative term. We conduct modified equation analysis on the CCD scheme and eliminate the leading discretization error terms for accurately predicting unidirectional wave propagation. The Fourier analysis is carried out as well on the proposed numerical scheme to minimize the dispersive error. For preserving Hamiltonians in Camassa-Holm equation, a symplecticity conserving time integrator has been employed. The other main emphasis of the present study is the use of u−P−α formulation to get nondissipative CH solution for peakon-antipeakon and soliton-anticuspon head-on wave collision problems.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.290914.030615a
Communications in Computational Physics, Vol. 19 (2016), Iss. 3 : pp. 603–631
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 29