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Notes on the numerical solution of the Benjamin equation

Dougalis, V ; Duran, A ; Mitsotakis, D; Mitsotakis, D (pacrepositoryorg)

arXiv.org, May 22, 2014

E-ISSN: 2331-8422

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  • Nhan đề:
    Notes on the numerical solution of the Benjamin equation
  • Tác giả: Dougalis, V ; Duran, A ; Mitsotakis, D
  • Mitsotakis, D (pacrepositoryorg)
  • Chủ đề: Partial Differential Equations ; Finite Element Method ; Surface Tension ; Mathematical Models ; Wave Propagation ; Stability ; Solitary Waves ; Internal Waves ; Partial Differential Equations
  • Là 1 phần của: arXiv.org, May 22, 2014
  • Mô tả: In this paper we consider the Benjamin equation, a partial differential equation that models one-way propagation of long internal waves of small amplitude along the interface of two fluid layers under the effects of gravity and surface tension. We solve the periodic initial-value problem for the Benjamin equation numerically by a new fully discrete hybrid finite-element / spectral scheme, which we first validate by pinning down its accuracy and stability properties. After testing the evolution properties of the scheme in a study of propagation of single - and multi-pulse solitary waves of the Benjamin equation, we use it in an exploratory mode to illuminate phenomena such as overtaking collisions of solitary waves, and the stability of single-, multi-pulse and 'depression' solitary waves.
  • Ngôn ngữ: English
  • Số nhận dạng: E-ISSN: 2331-8422

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