Advertisement

Journal of Scientific Computing

, Volume 17, Issue 1–4, pp 143–152 | Cite as

A Discontinuous Spectral Element Model for Boussinesq-Type Equations

  • C. Eskilsson
  • S. J. Sherwin
Article

Abstract

We present a discontinuous spectral element model for simulating 1D nonlinear dispersive water waves, described by a set of enhanced Boussinesq-type equations. The advective fluxes are calculated using an approximate Riemann solver while the dispersive fluxes are obtained by centred numerical fluxes. Numerical computation of solitary wave propagation is used to prove the exponential convergence.

discontinuous spectral element method Boussinesq-type equations 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. Cockburn, B., and Shu, C.-W. (1998). The local discontinuous Galerkin method for time-dependent convection-diffusion systems. SIAM J. Numer. Anal. 35(6), 2440–2463.Google Scholar
  2. Eskilsson, C., and Sherwin, S. J. (2002). A spectral element method for Boussinesq-type equations. IC Aero Report 02–01.Google Scholar
  3. Madsen, P. A., and Schäffer, H. A. (1998). Higher-order Boussinesq-type equations for surface gravity waves: Derivation and analysis. Philos. Trans. Roy. Soc. London Ser. A 356, 3123–3184.Google Scholar
  4. Nwogu, O. (1993). Alternative form of Boussinesq equations for near shore wave propagation. J. Waterway, Port, Coastal and Ocean Engrg. 199, 618–638.Google Scholar
  5. Toro, E. F. (2001). Shock-Capturing Methods for Free-Surface Shallow Flows, John Wiley & Sons.Google Scholar
  6. Wei, G., and Kirby, J. T. (1995). Time-dependent numerical code for extended Boussinesq equations. J. of Waterway, Port, Coastal and Ocean Engrg. 121(5), 251–261.Google Scholar
  7. Yan, J., and Shu, C.-W. (2001). A local discontinuous Galerkin method for KdV type equations. Submitted to SIAM J. Numer. Anal. Google Scholar

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • C. Eskilsson
    • 1
  • S. J. Sherwin
    • 2
  1. 1.Water Environment TransportChalmers University of TechnologyGothenburgSweden
  2. 2.Department of AeronauticsImperial College of Science, Technology and MedicineLondonUnited Kingdom

Personalised recommendations