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Central-Upwind Schemes for Boussinesq Paradigm Equations

  • Alina Chertock
  • Christo I. Christov
  • Alexander Kurganov
Part of the Notes on Numerical Fluid Mechanics and Multidisciplinary Design book series (NNFM, volume 115)

Abstract

We develop a new accurate and robust numerical method for the Boussinesq paradigm equation (BPE). To design the method we first introduce a change of variables, for which the BPE takes the form of a nonlinear wave equation with the global pressure, and rewrite the wave equation as a system of conservation laws with a global flux. We then apply a Godunov-type central-upwind scheme together with an efficient FFT-based elliptic solver to the resulting system. Making use of the new scheme, we investigate the propagation of one- and two-dimensional solitary waves of BPE and identify their solitonic behaviour.

Keywords

Solitary Wave Soliton Solution Phase Speed Helmholtz Equation Nonlinear Wave Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Alina Chertock
    • 1
  • Christo I. Christov
    • 2
  • Alexander Kurganov
    • 3
  1. 1.Department of MathematicsNorth Carolina State UniversityRaleighUSA
  2. 2.Department of MathematicsUniversity of LouisianaLafayetteUSA
  3. 3.Mathematics DepartmentTulane UniversityNew OrleansUSA

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