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Numerical Approximation of NS-TKE Model

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Mathematical and Numerical Foundations of Turbulence Models and Applications

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Abstract

In this chapter we perform the numerical analysis of finite element approximations of the NS-TKE model. We consider truncated eddy viscosities and production term so as a smooth friction boundary condition for the TKE. In the steady case we prove stability and strong convergence to a weak solution. In the evolution case we consider a semi-implicit Euler scheme that decouples velocity and TKE. We prove the stability of the scheme and weak convergence to a limit problem in which the TKE only verifies a variational inequality.

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Authors and Affiliations

  1. Department of Differential Equations and Numerical Analysis and Institute of Mathematics (IMUS), University of Seville, Seville, Spain

    Tomás Chacón Rebollo

  2. Institute of Mathematical Research of Rennes, IRMAR - UMR 6625, CNRS, University of Rennes 1, Rennes, France

    Roger Lewandowski

Authors
  1. Tomás Chacón Rebollo
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  2. Roger Lewandowski
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Chacón Rebollo, T., Lewandowski, R. (2014). Numerical Approximation of NS-TKE Model. In: Mathematical and Numerical Foundations of Turbulence Models and Applications. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4939-0455-6_12

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