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A variational principle for the Navier-Stokes equations incorporating finite element approximation to high-Re flows. (English) Zbl 0977.76053

A variational principle is proposed to construct a finite element approximation for two-dimensional Navier-Stokes steady cavity lid-driven flows. The discrete equations are solved by a multigrid method. Solutions are constructed for the Reynolds number in the range between 1000 and 10000 on a uniform rectangular mesh consisting of \(120\times 120\) grid points.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76M30 Variational methods applied to problems in fluid mechanics
35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
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