BIT Numerical Mathematics

, Volume 43, Issue 1, pp 41–55

Conservation Properties of Smoothed Particle Hydrodynamics Applied to the Shallow Water Equation

  • Jason Frank
  • Sebastian Reich

DOI: 10.1023/A:1023620100065

Cite this article as:
Frank, J. & Reich, S. BIT Numerical Mathematics (2003) 43: 41. doi:10.1023/A:1023620100065


Kelvin's circulation theorem and its implications for potential vorticity (PV) conservation are among the most fundamental concepts in ideal fluid dynamics. In this note, we discuss the numerical treatment of these concepts with the Smoothed Particle Hydrodynamics (SPH) and related methods. We show that SPH satisfies an exact circulation theorem in an interpolated velocity field, and that, when appropriately interpreted, this leads to statements of conservation of PV and generalized enstrophies. We also indicate some limitations where the analogy with ideal fluid dynamics breaks down.

Geophysical fluid dynamics potential vorticity conserving methods geometric methods smoothed particle hydrodynamics 

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Jason Frank
    • 1
  • Sebastian Reich
    • 2
  1. 1.CWIAmsterdam
  2. 2.Department of MathematicsImperial College

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