Three-dimensional simulation of a lake using a Penalty Stabilized time-marching algorithm

T. Chacón Rebollo ^[1] ; D. Rodríguez Gómez ^[1]
1. [1] Universidad de Sevilla
  
  Universidad de Sevilla
  
  Sevilla, España
Localización: XVII Congreso de Ecuaciones Diferenciales y Aplicaciones ; VII Congreso de Matemática Aplicada: Salamanca, 14-28 septiembre 2001 / coord. por Luis Ferragut Canals, Anastasio Pedro Santos Yanguas, 2001, ISBN 8469961446, págs. 393-394
Idioma: inglés
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Resumen
- One of the major problems related to computational simulations of three - dimensional (3D) geophysical fluids is the need of large amounts of degrees of freedom, what produces codes with very high computational complexity. Our aim in this paper is to introduce a method requiring a reduced amount of degrees of freedom, able to accurately reproduce the main features of unsteady 3D flows arising in Oceanography. We use a reduced formulation of the Primitive Equations of the Ocean, which only includes the (3D) horizontal velocity and the (2D) surface pressure (cf. [4]). We introduce a semi-implicit Backward Euler scheme for the time discretization. The spatial discretization in each time step is carried out through a family of Stabilized Methods in order to circumvent the use of pairs of spaces satisfying the inf-sup condition, thus attempting a large saving of degrees of freedom. We show a numerical test in a real-life application. Specifically, we simulate the wind-driven circulation in the lake Leman (Switzerland).