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Numerical approximation of the Smagorinsky turbulence model applied to the primitive equations of the ocean

Author

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  • Chacón Rebollo, Tomás
  • Hecht, Frédéric
  • Gómez Mármol, Macarena
  • Orzetti, Giordano
  • Rubino, Samuele

Abstract

This paper deals with the development of efficient numerical solvers for the primitive equations of the ocean in turbulent regime. We derive the numerical approximation of a reduced model by the Smagorinsky turbulence model that includes stabilization of the pressure discretization by a penalty technique. We perform the numerical analysis of this discretization (stability, convergence, error estimates), obtaining error estimates of at most first order in natural norms, due to the penalty structure of the Smagorinsky eddy viscosity. We finally perform some numerical tests for the primitive and Navier–Stokes equations, that confirm the theoretical convergence expectations.

Suggested Citation

  • Chacón Rebollo, Tomás & Hecht, Frédéric & Gómez Mármol, Macarena & Orzetti, Giordano & Rubino, Samuele, 2014. "Numerical approximation of the Smagorinsky turbulence model applied to the primitive equations of the ocean," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 99(C), pages 54-70.
    • Handle: RePEc:eee:matcom:v:99:y:2014:i:c:p:54-70
    DOI: 10.1016/j.matcom.2013.04.023
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    Cited by:

    1. Rubino, Samuele, 2019. "An efficient time-splitting approximation of the Navier–Stokes equations with LPS modeling," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 318-337.

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