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)


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.


Solitary Wave Soliton Solution Phase Speed Helmholtz Equation Nonlinear Wave Equation 
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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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