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Numerical simulation of Camassa-Holm peakons by adaptive upwinding

Artebrant, Robert LU and Schroll, Achim LU (2006) In Applied Numerical Mathematics 56(5). p.695-711
Abstract
The Camassa-Holm equation is a conservation law with a non-local flux that models shallow water waves and features soliton solutions with a corner at their crests, so-called peakons. In the present paper a finite-volume method is developed to simulate the dynamics of peakons. This conservative scheme is adaptive, high resolution and stable without any explicit introduction of artificial viscosity. A numerical simulation indicates that a certain plateau shaped travelling wave solution breaks up in time. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.
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type
Contribution to journal
publication status
published
subject
keywords
Camassa-Holm equation, peakon dynamics, adaptive finite-volume method
in
Applied Numerical Mathematics
volume
56
issue
5
pages
695 - 711
publisher
Elsevier
external identifiers
  • wos:000236426000007
  • scopus:33644862175
ISSN
0168-9274
DOI
10.1016/j.apnum.2005.06.002
language
English
LU publication?
yes
additional info
The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Numerical Analysis (011015004), Centre for Mathematical Sciences (011015000)
id
dd911d39-52f1-4260-b8fd-91f6b2f66274 (old id 414940)
date added to LUP
2016-04-01 16:58:47
date last changed
2021-08-25 01:38:26
@article{dd911d39-52f1-4260-b8fd-91f6b2f66274,
  abstract     = {The Camassa-Holm equation is a conservation law with a non-local flux that models shallow water waves and features soliton solutions with a corner at their crests, so-called peakons. In the present paper a finite-volume method is developed to simulate the dynamics of peakons. This conservative scheme is adaptive, high resolution and stable without any explicit introduction of artificial viscosity. A numerical simulation indicates that a certain plateau shaped travelling wave solution breaks up in time. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.},
  author       = {Artebrant, Robert and Schroll, Achim},
  issn         = {0168-9274},
  language     = {eng},
  number       = {5},
  pages        = {695--711},
  publisher    = {Elsevier},
  series       = {Applied Numerical Mathematics},
  title        = {Numerical simulation of Camassa-Holm peakons by adaptive upwinding},
  url          = {http://dx.doi.org/10.1016/j.apnum.2005.06.002},
  doi          = {10.1016/j.apnum.2005.06.002},
  volume       = {56},
  year         = {2006},
}