Optimization of Lakes Aeration Process

Authors: Mohamed Abdelwahed

Abstract:

The aeration process via injectors is used to combat the lack of oxygen in lakes due to eutrophication. A 3D numerical simulation of the resulting flow using a simplified model is presented. In order to generate the best dynamic in the fluid with respect to the aeration purpose, the optimization of the injectors location is considered. We propose to adapt to this problem the topological sensitivity analysis method which gives the variation of a criterion with respect to the creation of a small hole in the domain. The main idea is to derive the topological sensitivity analysis of the physical model with respect to the insertion of an injector in the fluid flow domain. We propose in this work a topological optimization algorithm based on the studied asymptotic expansion. Finally we present some numerical results, showing the efficiency of our approach

Keywords: Quasi Stokes equations, Numerical simulation, topological optimization, sensitivity analysis.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1073417

References:

[1] M. Abdelwahed, M. Amara, F. Dabaghi, Numerical analysis of a two phase flow, Journal of Computational Methods, 5(3), 2012.
[2] M. Abdelwahed, F. Dabaghi, D. Ouazar, A virtual numerical simulator for aeration effects in lake eutrophication, Int. J. Comput. Fluid. Dynamics. 16(2), 119-128, 2002.
[3] D. Arnold, F. Brezzi, M. Fortin, A stable finite element for the Stokes equations,Calcolo 21(4),337-344, 1984.
[4] E. Clement, Dispertion de bulles et modifications du mouvement de la phase porteuse dans des 'ecoulements tourbillonnaires, Phd Thesis, Institut Nationale polytechnique de Toulouse, 1999.
[5] D. Legende, Quelques aspects des forces hydrodynamiques et des transferts de chaleur sur une bulle sph'erique, Phd thesis, INP Toulouse, France, 1996.
[6] Ph. Guillaume, K. Sid Idris, Topological sensitivity and shape optimization for the Stokes equations, SIAM J. Control Optim. 43(1), 1-31, 2004.
[7] M. Hassine, S. Jan, M. Masmoudi, From differential calculus to 0 − 1 topological optimization, SIAM J. Cont. Optim. 45(6), 1965-1987, 2007.
[8] M. Hassine, M. Masmoudi, The topological asymptotic expansion for the Quasi-Stokes problem, ESAIM, COCV J. 10(4), 478-504, 2004.
[9] M. Ishii, Thermo-fluid dynamic theory of a two-phase flow, Collection de la direction des 'etudes de recherche d-'electricit'e de france, EYROLLES, 1975.
[10] J. Sokolowski, A. Zochowski, On the topological derivative in shape optimization, SIAM J. Control Optim. 37(4) ,1251-1272 ,1999.