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

Johnson, Claes; Saranen, Jukka

Math. Comput. 47, 1-18 (1986).

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:

76D05	Navier-Stokes equations for incompressible viscous fluids
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35Q30	Navier-Stokes equations

Keywords:

streamline diffusion method; finite element method; convection-dominated convection-diffusion problems; time-dependent two-dimensional Navier- Stokes equations; incompressible Newtonian flow; Euler equations; stream function-vorticity formulation; velocity-pressure formulation; velocity- pressure-vorticity formulation