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A Stability Analysis of a Eulerian Method for Some Surface Gravity Wave Problems

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Nonlinear Hyperbolic Equations — Theory, Computation Methods, and Applications

Part of the book series: Notes on Numerical Fluid Mechanics ((NNFM,volume 24))

Summary

For the solution of some surface gravity water wave problems a Eulerian method is given as a system of 2N ordinary differential equations where the moving boundary is described by means of N “Eulerian” points. Part of a stability analysis of the system has been carried out with respect to equilibrium solutions, periodic solutions, and numerical solutions. Numerical experiments with the system have not disclosed unprovoked saw-tooth instabilities, which have plagued some other methods.

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Authors and Affiliations

  1. Laboratory of Applied Mathematical Physics, The Technical University of Denmark, DK-2800, Lyngby, Denmark

    Søren Christiansen

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  1. Søren Christiansen
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Editors and Affiliations

  1. Lehr- und Forschungsgebiet Mechanik, RWTH Aachen, Templergraben 64, 5100, Aachen, Germany

    Josef Ballmann

  2. Institut für Geometric und Praktische Mathematik, RWTH Aachen, Templergraben 55, 5100, Aachen, Germany

    Rolf Jeltsch

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© 1989 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig

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Christiansen, S. (1989). A Stability Analysis of a Eulerian Method for Some Surface Gravity Wave Problems. In: Ballmann, J., Jeltsch, R. (eds) Nonlinear Hyperbolic Equations — Theory, Computation Methods, and Applications. Notes on Numerical Fluid Mechanics, vol 24. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-87869-4_8

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  • DOI: https://doi.org/10.1007/978-3-322-87869-4_8

  • Publisher Name: Vieweg+Teubner Verlag

  • Print ISBN: 978-3-528-08098-3

  • Online ISBN: 978-3-322-87869-4

  • eBook Packages: Springer Book Archive

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