A 2D model for hydrodynamics and biology coupling applied to algae growth simulations
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 5, p. 1387-1412

Cultivating oleaginous microalgae in specific culturing devices such as raceways is seen as a future way to produce biofuel. The complexity of this process coupling non linear biological activity to hydrodynamics makes the optimization problem very delicate. The large amount of parameters to be taken into account paves the way for a useful mathematical modeling. Due to the heterogeneity of raceways along the depth dimension regarding temperature, light intensity or nutrients availability, we adopt a multilayer approach for hydrodynamics and biology. For free surface hydrodynamics, we use a multilayer Saint-Venant model that allows mass exchanges, forced by a simplified representation of the paddlewheel. Then, starting from an improved Droop model that includes light effect on algae growth, we derive a similar multilayer system for the biological part. A kinetic interpretation of the whole system results in an efficient numerical scheme. We show through numerical simulations in two dimensions that our approach is capable of discriminating between situations of mixed water or calm and heterogeneous pond. Moreover, we exhibit that a posteriori treatment of our velocity fields can provide lagrangian trajectories which are of great interest to assess the actual light pattern perceived by the algal cells and therefore understand its impact on the photosynthesis process.

DOI : https://doi.org/10.1051/m2an/2013072
Classification:  35Q35,  35Q92,  76D05,  76Z99
Keywords: hydrostatic Navier-Stokes equations, Saint-Venant equations, free surface stratified flows, multilayer system, kinetic scheme, droop model, raceway, hydrodynamics and biology coupling, algae growth
     author = {Bernard, Olivier and Boulanger, Anne-C\'eline and Bristeau, Marie-Odile and Sainte-Marie, Jacques},
     title = {A 2D model for hydrodynamics and biology coupling applied to algae growth simulations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {47},
     number = {5},
     year = {2013},
     pages = {1387-1412},
     doi = {10.1051/m2an/2013072},
     mrnumber = {3100768},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2013__47_5_1387_0}
Bernard, Olivier; Boulanger, Anne-Céline; Bristeau, Marie-Odile; Sainte-Marie, Jacques. A 2D model for hydrodynamics and biology coupling applied to algae growth simulations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 5, pp. 1387-1412. doi : 10.1051/m2an/2013072. http://www.numdam.org/item/M2AN_2013__47_5_1387_0/

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