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Finite Element Solution of the Primitive Equations of the Ocean by the Orthogonal Sub-Scales Method

In: Numerical Mathematics and Advanced Applications 2009

Author

Listed:
  • Tomás Chacón Rebollo

    (Universidad de Sevilla. Facultad de Matemáticas. C/ Tarfia, Dpto. de Ecuaciones Diferenciales y Análisis Numérico)

  • Macarena Gómez Mármol

    (Universidad de Sevilla. Facultad de Matemáticas. C/ Tarfia, Dpto. de Ecuaciones Diferenciales y Análisis Numérico)

  • Isabel Sánchez Munoz

    (Escuela Universitaria de Ingeniería Técnica de Agrícola, Dpto. de Matemática Aplicada I)

Abstract

This paper introduces a method for the numerical solution of steady Primitive Equations of the Ocean. This is an adaptation of the Orthogonal Subscales – Variational Multiscale Method, using conforming finite elements. We choose this method on one hand because it is a stabilized method, thus providing a low-cost and accurate discretization. On another hand, because it also is a LES turbulence model, so no further turbulence modeling is needed. We perform a numerical analysis of stability and convergence by means of representation of stabilizing terms in spaces of bubble finite elements. In particular, we give an original proof of the inf-sup condition to estimate the surface pressure. We present some numerical experiments for 2D flows that confirm the theoretical expectations.

Suggested Citation

  • Tomás Chacón Rebollo & Macarena Gómez Mármol & Isabel Sánchez Munoz, 2010. "Finite Element Solution of the Primitive Equations of the Ocean by the Orthogonal Sub-Scales Method," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 245-252, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_25
    DOI: 10.1007/978-3-642-11795-4_25
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