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

Tomás Chacón Rebollo (), Macarena Gómez Mármol () and Isabel Sánchez Munoz ()
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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

A chapter in Numerical Mathematics and Advanced Applications 2009, 2010, pp 245-252 from Springer

Abstract: 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.

Keywords: Surface Pressure; Horizontal Velocity; Convex Domain; Primitive Equation; Bubble Function (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-11795-4_25

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DOI: 10.1007/978-3-642-11795-4_25

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