Section: New Results

Modelling of complex flows

Modelling and simulation of sediment transport

Participants : Emmanuel Audusse, Léa Boittin, Martin Parisot, Jacques Sainte-Marie.

Following previous works, a numerical scheme for the sediment layer is proposed and assessed. The influence of the viscosity on the behaviour of the sediment layer is studied. A numerical strategy for the resolution of the coupled model (water layer and sediment layer) is implemented. The behaviour of the coupled system is numerically assessed. Academic test cases are performed.

Modelling of photosynthesis through microalgae cultivation

Participants : Marie-Odile Bristeau, Jacques Sainte-Marie.

In collaboration with O. Bernard.

In the present multidisciplinary downscaling study, we reconstruct single cell trajectories in an open raceway and experimentally reproduce the according high frequency light pattern to observe its effect on the growth of Dunaliella salina. We show that the frequency of such a realistic signal plays a decisive role on the dynamics of photosynthesis, which reveal an unexpected photosynthetic response compared to that recorded under the on/off signals usually used in the literature. This study highlights the need for experiments with more realistic light stimuli in order to better understand microalgal growth at high cell density. We also propose an experimental protocol with simple piecewise constant, yet more realistic, light fluctuations.

Buoyancy modelling

Participants : Edwige Godlewski, Martin Parisot, Jacques Sainte-Marie, Fabien Wahl.

Firstly, the work of the previous year was completed and lead to the submission of an article [38]. More precisely the fixed point algorithm is rewritten using a new unknown. This allows to increase the numerical robustness and accuracy of the scheme. The proposed resolution is assessed on several stationary and non-stationary test cases with analytical solutions.

In the continuity of this work, the modelling of fluid-structure interaction resolution is added in the previous work in order to simulate floating structures for marine energy devices. In a first step only the vertical movement is studied, with no major scientific lock. In a second time the horizontal movement of the structure is considered and required a deeper analysis to ensure the entropy-stability at the discrete level.

A Free Interface Model for Static/Flowing Dynamics in Thin-Layer Flows of Granular Materials with Yield: Simple Shear Simulations and Comparison with Experiments

Participant : Anne Mangeney.

In collaboration with C. Lusso, F. Bouchut, A. Ern.

Flows of dense granular materials comprise regions where the material is flowing, and regions where it is static. In [15], we introduce two numerical methods to deal with the particular formulation of this model with a free interface. They are used to evaluate the respective role of yield and viscosity for the case of a constant source term, which corresponds to simple shear viscoplastic flows. Both the analytical solution of the inviscid model and the numerical solution of the viscous model (with a constant viscosity or the variable viscosity of the $\mu \left(I\right)$-rheology) are compared with experimental data.

Metamodelling of a road traffic assignment model

Participant : Vivien Mallet.

In collaboration with R. Chen, V. Aguiléra, F. Cohn, D. Poulet, F. Brocheton.

We proposed a metamodelling approach to design a close approximation to the traffic model, but with a very low computational cost. It consists in a dimensionality reduction of the model outputs by principal component analysis and a statistical emulation relying on regression and interpolation between training samples. A case study was carried out for the agglomeration of Clermont-Ferrand (France). Compared with traffic flow measurements, the performance of the metamodel is similar to that of the complete model during a one-month period, but the computational time decreases from 2 days on 110 cores to less than 1 minute on one core.