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Streamline diffusion methods for the incompressible Euler and Navier- Stokes equations. (English) Zbl 0609.76020

The authors extend the streamline diffusion method, which is a finite element method for convection-dominated convection-diffusion problems, to the time-dependent two-dimensional Navier-Stokes equations for an incompressible Newtonian flow in the case of high Reynolds number and also the limit case with zero viscosity, the Euler equations.

The method for the Euler equations is based on using the stream function- vorticity formulation of the Euler equations. Two methods are considered for the Navier-Stokes equation: one method using a velocity-pressure formulation, and one method using a velocity-pressure-vorticity formulation.

Reviewer: J.Groß

MSC:
76D05Navier-Stokes equations (fluid dynamics)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
35Q30Stokes and Navier-Stokes equations