scholarly journals A finite element discretization of the three-dimensional Navier–Stokes equations with mixed boundary conditions

2009 ◽  
Vol 43 (6) ◽  
pp. 1185-1201 ◽  
Author(s):  
Christine Bernardi ◽  
Frédéric Hecht ◽  
Rüdiger Verfürth
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Stokes Equations ◽  
Mixed Boundary ◽  
Three Dimensional ◽  
Mixed Boundary Conditions ◽  
Navier Stokes ◽  
Finite Element Discretization ◽  
Navier Stokes Equations ◽  
Element Discretization

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.

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