Numerical solution of the Primitive Equations of the ocean by the Orthogonal Sub-Scales VMS method

  • Authors:

  • Tomás Chacón Rebollo;Macarena Gómez Mármol;Isabel Sánchez Muñoz

  • Affiliations:

  • Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Spain;Dpto. de Matemática Aplicada I, Universidad de Sevilla, Spain;Dpto. de Matemática Aplicada I, Universidad de Sevilla, Spain

  • Venue:
  • Applied Numerical Mathematics
  • Year:
  • 2012

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Abstract

This paper deals with the development of efficient numerical solvers for the Primitive Equations of the ocean. We consider weak solutions of a reduced model that includes the horizontal velocity and the surface pressure. We derive the numerical approximation of this model by the Orthogonal Sub-Scales (OSS) method via finite elements discretization. We perform the numerical analysis of this discretization (stability, convergence, error estimates) for a linearized model, obtaining optimal error estimates for 2D flows. This analysis is based upon a specific inf-sup condition for the OSS discretization. We also perform some numerical tests for the non-linear Primitive Equations, that confirm the theoretical convergence order expectations, and show an improved convergence with respect to standard mixed methods.