The hyperbolic relaxation systems for the forced KdV equations with hydraulic falls

Heesun Choi; Hongjoong Kim

doi:10.1016/j.euromechflu.2016.03.002

The hyperbolic relaxation systems for the forced KdV equations with hydraulic falls

Heesun Choi, Hongjoong Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

This paper suggests hyperbolic relaxation system as a new efficient way in finding various types of numerical solutions of forced Korteweg-de Vries (fKdV) equations. When non-periodic numerical solutions such as hydraulic falls of fKdV equations with bumps are considered, the application of the spectral method or the finite difference methods may not work properly. As an alternative, the relaxation method has been applied to obtain the hyperbolic system for fKdV equations. The computational results show that the derived relaxation systems capture both hydraulic falls and solitary-type solutions accurately without numerical oscillations and require much less computational costs than other methods.

Original language	English
Pages (from-to)	20-28
Number of pages	9
Journal	European Journal of Mechanics, B/Fluids
Volume	58
DOIs	https://doi.org/10.1016/j.euromechflu.2016.03.002
Publication status	Published - 2016 Jul

Bibliographical note

Funding Information:
This research of Kim was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-2014R1A1A2058271 ).

Publisher Copyright:
© 2016 Elsevier Masson SAS. All rights reserved.

Keywords

Conservation laws
Forced Korteweg-de Vries equation
Hydraulic falls
Relaxation method

ASJC Scopus subject areas

Mathematical Physics
General Physics and Astronomy

Access to Document

10.1016/j.euromechflu.2016.03.002

Cite this

@article{c28753ba27fd4d5dbd9c1b4703463e2e,

title = "The hyperbolic relaxation systems for the forced KdV equations with hydraulic falls",

abstract = "This paper suggests hyperbolic relaxation system as a new efficient way in finding various types of numerical solutions of forced Korteweg-de Vries (fKdV) equations. When non-periodic numerical solutions such as hydraulic falls of fKdV equations with bumps are considered, the application of the spectral method or the finite difference methods may not work properly. As an alternative, the relaxation method has been applied to obtain the hyperbolic system for fKdV equations. The computational results show that the derived relaxation systems capture both hydraulic falls and solitary-type solutions accurately without numerical oscillations and require much less computational costs than other methods.",

keywords = "Conservation laws, Forced Korteweg-de Vries equation, Hydraulic falls, Relaxation method",

author = "Heesun Choi and Hongjoong Kim",

note = "Funding Information: This research of Kim was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-2014R1A1A2058271 ). Publisher Copyright: {\textcopyright} 2016 Elsevier Masson SAS. All rights reserved.",

year = "2016",

month = jul,

doi = "10.1016/j.euromechflu.2016.03.002",

language = "English",

volume = "58",

pages = "20--28",

journal = "European Journal of Mechanics, B/Fluids",

issn = "0997-7546",

publisher = "Elsevier BV",

}

TY - JOUR

T1 - The hyperbolic relaxation systems for the forced KdV equations with hydraulic falls

AU - Choi, Heesun

AU - Kim, Hongjoong

N1 - Funding Information: This research of Kim was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-2014R1A1A2058271 ). Publisher Copyright: © 2016 Elsevier Masson SAS. All rights reserved.

PY - 2016/7

Y1 - 2016/7

N2 - This paper suggests hyperbolic relaxation system as a new efficient way in finding various types of numerical solutions of forced Korteweg-de Vries (fKdV) equations. When non-periodic numerical solutions such as hydraulic falls of fKdV equations with bumps are considered, the application of the spectral method or the finite difference methods may not work properly. As an alternative, the relaxation method has been applied to obtain the hyperbolic system for fKdV equations. The computational results show that the derived relaxation systems capture both hydraulic falls and solitary-type solutions accurately without numerical oscillations and require much less computational costs than other methods.

AB - This paper suggests hyperbolic relaxation system as a new efficient way in finding various types of numerical solutions of forced Korteweg-de Vries (fKdV) equations. When non-periodic numerical solutions such as hydraulic falls of fKdV equations with bumps are considered, the application of the spectral method or the finite difference methods may not work properly. As an alternative, the relaxation method has been applied to obtain the hyperbolic system for fKdV equations. The computational results show that the derived relaxation systems capture both hydraulic falls and solitary-type solutions accurately without numerical oscillations and require much less computational costs than other methods.

KW - Conservation laws

KW - Forced Korteweg-de Vries equation

KW - Hydraulic falls

KW - Relaxation method

UR - http://www.scopus.com/inward/record.url?scp=84962766747&partnerID=8YFLogxK

U2 - 10.1016/j.euromechflu.2016.03.002

DO - 10.1016/j.euromechflu.2016.03.002

M3 - Article

AN - SCOPUS:84962766747

SN - 0997-7546

VL - 58

SP - 20

EP - 28

JO - European Journal of Mechanics, B/Fluids

JF - European Journal of Mechanics, B/Fluids

ER -

The hyperbolic relaxation systems for the forced KdV equations with hydraulic falls

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this