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Automatic insertion of a turbulence model in the finite element discretization of the Navier-Stokes equations

Abstract : 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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https://hal.archives-ouvertes.fr/hal-00173706
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Christine Bernardi, Tomas Chacon-Rebollo, Frédéric Hecht, Roger Lewandowski. Automatic insertion of a turbulence model in the finite element discretization of the Navier-Stokes equations. Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2009, 19 (7), pp.1139-1183. ⟨10.1142/S0218202509003747⟩. ⟨hal-00173706⟩

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