scholarly journals AUTOMATIC INSERTION OF A TURBULENCE MODEL IN THE FINITE ELEMENT DISCRETIZATION OF THE NAVIER–STOKES EQUATIONS

2009 ◽  
Vol 19 (07) ◽  
pp. 1139-1183 ◽  
Author(s):  
CHRISTINE BERNARDI ◽  
TOMÁS CHACÓN REBOLLO ◽  
FRÉDÉRIC HECHT ◽  
ROGER LEWANDOWSKI
Keyword(s):  
Finite Element ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Stokes Equations ◽  
A Posteriori Error Estimates ◽  
Navier Stokes ◽  
Mesh Adaptivity ◽  
Finite Element Discretization ◽  
Navier Stokes Equations ◽  
Element Discretization

We consider the finite element discretization of the Navier–Stokes equations locally coupled with the equation for the turbulent kinetic energy through an eddy viscosity. We prove a posteriori error estimates which allow to automatically determine the zone where the turbulent kinetic energy must be inserted in the Navier–Stokes equations and also to perform mesh adaptivity in order to optimize the discretization of these equations. Numerical results confirm the interest of such an approach.

Numerical calculations of the primary-flow exchange process in the Taylor problem

1988 ◽  
Vol 197 ◽  
pp. 57-79 ◽  
Author(s):  
K. A. Cliffe
Keyword(s):  
Stokes Equations ◽  
Exchange Process ◽  
Numerical Calculations ◽  
Navier Stokes ◽  
Finite Element Discretization ◽  
Primary Flow ◽  
Navier Stokes Equations ◽  
Element Discretization ◽  
Taylor Problem ◽  
Solution Surface

Numerical methods are used to study the way in which the number of cells present in the Taylor experiment changes as the length of the comparatively short annulus varies. The structure of the solution surface is determined by following paths of singular points in a finite-element discretization of the axisymmetric Navier–Stokes equations. The numerical results are compared with the experiments of Benjamin (1978b), Mullin (1982) and Mullin et al. (1982). The calculations are in agreement with the qualitative theory of Benjamin (1978a) and Schaeffer (1980) except that in the interaction involving four- and six-cell flows, the numerical calculations indicate that the six-cell flow can become unstable owing to perturbations that are antisymmetric about the midplane.

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