Evolutionary NS-TKE Model

  • Tomás Chacón Rebollo
  • Roger Lewandowski
Chapter
First Online:
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)

Abstract

We study the NS-TKE model with a wall law for the velocity v and the homogenous boundary condition for the TKE k. The abstract variational framework is specified, and a series of a priori narrow estimates is derived. The model is approximated by interconnected approximate Leray-α-like models, in which transport terms are regularized by convolution, the source term, and wall law by truncation. We show that the corresponding families of variational problems admit solutions and converge to one another. In the final step of the process, we obtain an NS-TKE model yielding an inequality for the TKE. This chapter finishes with a thorough bibliographical section on the 3D evolutionary Navier–Stokes equations.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Tomás Chacón Rebollo
    • 1
  • Roger Lewandowski
    • 2
  1. 1.Department of Differential Equations and Numerical Analysis and Institute of Mathematics (IMUS)University of SevilleSevilleSpain
  2. 2.Institute of Mathematical Research of Rennes, IRMAR - UMR 6625, CNRSUniversity of Rennes 1RennesFrance

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