Convergence of the grid-free point vortex method for the three-dimensional Euler equations

Georges Henri Cottet, Jonathan Goodman, Thomas Y. Hou

Research output: Contribution to journalArticle

Abstract

Convergence of the grid-free point vortex method is proved for three-dimensional Euler equations with smooth solutions. Two new techniques are used to obtain consistency and stability of the method. The first one is Strang's trick which allows smooth approximate solutions to be constructed to the vortex method equations with arbitrarily small errors. This result is used to obtain consistency and nonlinear stability. The second tool is the use of a very special discrete negative norm in l1 space for vorticity which gives rise to the linear stability result. Combining these two techniques proves uniform convergence of the method with second-order accuracy.

Original languageEnglish (US)
Pages (from-to)291-307
Number of pages17
JournalSIAM Journal on Numerical Analysis
Volume28
Issue number2
StatePublished - Apr 1991

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Vortex Method
Point Vortex
Euler equations
Euler Equations
Vortex flow
Grid
Three-dimensional
Second-order Accuracy
Nonlinear Stability
Linear Stability
Smooth Solution
Uniform convergence
Vorticity
Approximate Solution
Strings
Norm

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

Cite this

Convergence of the grid-free point vortex method for the three-dimensional Euler equations. / Cottet, Georges Henri; Goodman, Jonathan; Hou, Thomas Y.

In: SIAM Journal on Numerical Analysis, Vol. 28, No. 2, 04.1991, p. 291-307.

Research output: Contribution to journalArticle

Cottet, Georges Henri ; Goodman, Jonathan ; Hou, Thomas Y. / Convergence of the grid-free point vortex method for the three-dimensional Euler equations. In: SIAM Journal on Numerical Analysis. 1991 ; Vol. 28, No. 2. pp. 291-307.
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