Author(s)

J. Fe & F. Navarrina

Abstract

A second order finite volume model for the resolution of the two dimensional shallow water equationswith turbulent term is presented. It is shown that, if a first order upwind method is used to discretize the hydrodynamic equations, a considerable amount of numerical viscosity (or diffusion) is produced. For this reason a second order method has been developed, which makes use of the mean gradient of the variables in a cell. To compare the first and second order methods, the Cavity Flow problem is used. Then a backward step problem is solved, using the k − ε turbulence model to calculate the turbulent viscosity at every point. The results are compared with experimental measures and they confirm the good behavior of the model. Keywords: finite volumes, shallow water equations, numerical viscosity, turbulent term, gradient mean values.

Keywords

finite volumes, shallow water equations, numerical viscosity, turbulent term, gradient mean values.