Resumen de A P1 bubble/P1 finite element velocity-pressure solution of a pseudo homogeneous flow model simulating a two phase flow: application to lake eutrophication remedial by air injection

F. Dabaghi, Mohamed Amara, M. Abdelwahed

• The climatological variations, mainly and specifically thermal variations, generate in lakes an unsteady dynamic process making water quality decrease progressively; when the dissolved oxygen concentration reaches a low level, the lake is considered in eutrophication. The dynamic aeration process is one of the best remedial techniques against eutrophication. It consists in injecting air in the bottom of the lake. A good understanding of the eutrophication treatment through aeration requires a modeling based on a two phase ow (water-air bubbles) leading to many difficulties. In this paper, we describe the implementation of the aeration effect correction in a modified one-phase model to restitute as much as possible an equivalent behavior of the two-phase model. Preliminary studies of a mixed velocity-pressure formulation for 2D ows with variable density are presented in [1]. Using the characteristics method to approximate the total derivative convection term, the generic system is of Quasi-Stokes type. For the space discretization, we use the P1 bubble- P1 finite element method. Numerical experiments are then performed for scenario analysis.