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A ψ–ω finite element formulations for the Navier‐Stokes equations
Author(s) -
Dhatt Gouri,
Fomo Bonaventure Kamga,
Bourque Claude
Publication year - 1981
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620170205
Subject(s) - stream function , finite element method , mathematics , navier–stokes equations , extended finite element method , nonlinear system , vorticity , mathematical analysis , mixed finite element method , convergence (economics) , reynolds number , boundary value problem , stokes flow , flow (mathematics) , geometry , mechanics , physics , vortex , quantum mechanics , compressibility , turbulence , economics , thermodynamics , economic growth
A new method of solving the two‐dimensional Navier–Stokes equations by using the finite element method is proposed. The flow is represented by the stream function–vorticity formulation and the no‐slip boundary conditions are explicitly introduced in the nonlinear equations. This formulation coupled with the Newton‐Raphson method enables the study of stationary flows for high Reynolds number, without any convergence problem. A number of flow problems are analysed in order to demonstrate the efficiency of the present formulation.