Homogenization and convergence of the vortex method for 2‐D euler equations with oscillatory vorticity fields

Weinan E, Thomas Y. Hou

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

The 2‐D incompressible Euler equations with oscillatory vorticity fields are studied. A homogenization result for 2‐D Euler equations in velocity‐vorticity formulation is obtained and weak continuity of the equations is proved. Convergence of the vortex method is analyzed in the case when the continuous vorticity is not well resolved by the computational particles. Numerical results are given. Comparisons are made with the corresponding finite difference approximation.

Original languageEnglish (US)
Pages (from-to)821-855
Number of pages35
JournalCommunications on Pure and Applied Mathematics
Volume43
Issue number7
DOIs
StatePublished - Jan 1 1990
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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