A 2D model for hydrodynamics and biology coupling applied to algae growth simulations
1 Inria, team BioCore,
2 Inria, team ANGE, B.P. 105, 78153 Le Chesnay Cedex, France.
3 UPMC Univ Paris 06, CNRS UMR 7598, Laboratoire Jacques-Louis Lions, 75005, Paris, France.
4 CETMEF, 2 boulevard Gambetta, 60200 Compiègne, France.
Revised: 18 February 2013
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.
Mathematics Subject Classification: 35Q35 / 35Q92 / 76D05 / 76Z99
Key words: Hydrostatic Navier–Stokes equations / Saint–Venant equations / free surface stratified flows / multilayer system / kinetic scheme / droop model / raceway / hydrodynamics and biology coupling / algae growth
© EDP Sciences, SMAI, 2013