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On Formulations of Vorticity Systems for a Viscous Incompressible Flow with Numerical Applications
Author(s) -
Ruas V.
Publication year - 1994
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19940740112
Subject(s) - vorticity , vorticity equation , stream function , convergence (economics) , compressibility , incompressible flow , mathematics , finite element method , series (stratigraphy) , flow (mathematics) , burgers vortex , navier–stokes equations , classical mechanics , vortex , mathematical analysis , physics , mechanics , geometry , geology , thermodynamics , paleontology , economics , economic growth
The aim of this work is to present a series of analytical and numerical results related to vorticity formulations of the systems describing the motion of an incompressible viscous fluid. A rigorous variational framework for the two‐dimensional Stokes system is used as a basis in both the stream function‐vorticity and the velocity‐vorticity formulations. It is shown that this allows in particular a decoupled numerical solution method for the former formulation yielding optimal convergence results. On the other hand a new finite element scheme is proposed for the latter and illustrated by computer results. Finally a study on the velocity‐vorticity formulation in three dimensional space is carried out.