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A stabilized finite element formulation for the Reynolds-averaged Navier- Stokes equations. (English) Zbl 0817.76029

Summary: Stabilized finite element methods for the Navier-Stokes equations have matured into a powerful set of theoretical and algorithmic tools. These tools are described and further extended to account for turbulence. A one-equation model which preserves the symmetry of the system’s advective and diffusive matrices has been developed. This model utilizes a transport equation for the turbulent velocity scale and an algebraic relation for the turbulent length scale. From these two quantities an eddy viscosity can be calculated. This model has been implemented by way of a Galerkin/least-squares finite element method. Solutions are presented which verify the good behavior of the formulation.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76F10 Shear flows and turbulence