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Homogenization and convergence of the vortex method for 2‐D euler equations with oscillatory vorticity fields
Author(s) -
Weinan E,
Hou Thomas Y.
Publication year - 1990
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160430702
Subject(s) - vorticity , homogenization (climate) , euler equations , mathematics , vortex , vorticity equation , vortex stretching , mathematical analysis , burgers vortex , backward euler method , semi implicit euler method , compressibility , euler's formula , euler method , physics , mechanics , biodiversity , ecology , biology
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.