@Article{CiCP-19-603,
author = {},
title = {Development of a Combined Compact Difference Scheme to Simulate Soliton Collision in a Shallow Water Equation},
journal = {Communications in Computational Physics},
year = {2018},
volume = {19},
number = {3},
pages = {603--631},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.290914.030615a},
url = {http://global-sci.org/intro/article_detail/cicp/11102.html}
}