Conservation properties of Smoothed Particle Hydrodynamics applied to the shallow water equation

Jason Frank*, Sebastian Reich

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)41-55
Number of pages15
JournalBIT Numerical Mathematics
Volume43
Issue number1
DOIs
Publication statusPublished - Mar 2003
Externally publishedYes

Bibliographical note

Funding Information:
J. Frank gratefully acknowledges partial funding by GMD, Bonn. Partial financial support of S. Reich by EPSRC Grant GR/R09565/01 and by European Commission funding for the Research Training Network “Mechanics and Symmetry in Europe” is gratefully acknowledged.

Funding

J. Frank gratefully acknowledges partial funding by GMD, Bonn. Partial financial support of S. Reich by EPSRC Grant GR/R09565/01 and by European Commission funding for the Research Training Network “Mechanics and Symmetry in Europe” is gratefully acknowledged.

Keywords

  • Geometric methods
  • Geophysical fluid dynamics
  • Potential vorticity conserving methods
  • Smoothed particle hydrodynamics

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