## Extension to three-dimensional problems of the upwind finite element scheme based on the choice of up- and downwind points.(English)Zbl 0854.76051

Summary: A new upwind finite element scheme for the three-dimensional incompressible Navier-Stokes equations at high Reynolds numbers is presented. This three-dimensional scheme is a natural extension of the two-dimensional scheme [M. Tabata and S. Fujima, Int. J. Number. Methods Fluids 12, No. 4, 305-322 (1991; Zbl 0715.76012)] and has a potential to approximate the convection term with third-order accuracy. Stability domains in terms of a stabilizing parameter and the time increment appearing in the scheme are investigated numerically. The method of decomposition used for a tetrahedral element is also explained. Numerical results on flow problem in a lid-driven square cavity and past a circular cylinder are shown.

### MSC:

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

Zbl 0715.76012
Full Text:

### References:

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