Rotational Forms of Large Eddy Simulation Turbulence Models: Modeling and Mathematical Theory

Abstract

In this paper the authors present a derivation of a back-scatter rotational Large Eddy Simulation model, which is the extension of the Baldwin & Lomax model to non-equilibrium problems. The model is particularly designed to mathematically describe a fluid filling a domain with solid walls and consequently the differential operators appearing in the smoothing terms are degenerate at the boundary. After the derivation of the model, the authors prove some of the mathematical properties coming from the weighted energy estimates, which allow to prove existence and uniqueness of a class of regular weak solutions.

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Acknowledgements

The first author thanks Prof. Tatsien Li for the kind invitation to the conference “China-Italy Conference on PDEs and Their Applications” (Fudan Univ. Shanghai, PRC, Dec 9–13, 2019). The results of the paper have been developed also after discussion originated during the conference.

The second author thanks Prof. William J. Layton for bringing the Baldwin & Lomax model to his attention.

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Correspondence to Luigi C. Berselli or Roger Lewandowski or Dinh Duong Nguyen.

Additional information

This work was supported by the group GNAMPA of INdAM and the University of Pisa, under grant: PRA_2018_52 UNIPI.

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Berselli, L.C., Lewandowski, R. & Nguyen, D.D. Rotational Forms of Large Eddy Simulation Turbulence Models: Modeling and Mathematical Theory. Chin. Ann. Math. Ser. B 42, 17–40 (2021). https://doi.org/10.1007/s11401-021-0243-z

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Keywords

  • Fluid mechanics
  • Turbulence models
  • Rotational Large Eddy Simulation models
  • Navier-Stokes equations

2000 MR Subject Classification

  • 76D05
  • 35Q30
  • 76F65
  • 76D03
  • 35Q35