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

Tomás Chacón Rebollo , David Rodríguez Gómez

• 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).