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

Heesun Choi, Hongjoong Kim

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)20-28
Number of pages9
JournalEuropean Journal of Mechanics, B/Fluids
Volume58
DOIs
Publication statusPublished - 2016 Jul 1

Fingerprint

KdV Equation
Korteweg-de Vries Equation
Hydraulics
hydraulics
Numerical Solution
hyperbolic systems
Relaxation Method
spectral methods
Hyperbolic Systems
Spectral Methods
Difference Method
Computational Results
Computational Cost
Finite Difference
Oscillation
costs
oscillations
Alternatives

Keywords

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

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Mathematical Physics

Cite this

The hyperbolic relaxation systems for the forced KdV equations with hydraulic falls. / Choi, Heesun; Kim, Hongjoong.

In: European Journal of Mechanics, B/Fluids, Vol. 58, 01.07.2016, p. 20-28.

Research output: Contribution to journalArticle

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