Section: New Results

Modelling

Participants : Marie-Odile Bristeau, Jacques Sainte-Marie, Fabien Souillé, Emmanuel Audusse, Léa Boitin, Martin Parisot, Di Martino Bernard, Anne Mangeney.

How do microalgae perceive light in a high-rate pond? Towards more realistic Lagrangian experiments

In [10], we present a multidisciplinary downscaling study, where we first reconstructed single cell trajectories in an open raceway using an original hydrodynamical model offering a powerful discretization of the Navier–Stokes equations tailored to systems with free surfaces. The trajectory of a particular cell was selected and the associated high-frequency light pattern was computed. This light pattern was then experimentally reproduced in an Arduino-driven computer controlled cultivation system with a low density Dunaliella salina culture. The effect on growth and pigment content was recorded for various frequencies of the light pattern, by setting different paddle wheel velocities.

Modeling and simulation of sediment transport

A previous derivation of the sediment layer model has then been extended. Depending on the scaling chosen for the physical parameters, different models are obtained. The model we are interested in is the non-local model (with a viscosity term). Several numerical schemes are implemented and studied to simulate this model. Only one of these schemes is satisfactory. Simulations of the coupled water-sediment systems are made. The influence of the viscosity is emphasized. Turning on the non-local term allows to simulate dune growth and propagation.

Following the previous work, a numerical scheme for the sediment layer is proposed. The numerical scheme is tested. 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.

The Navier-Stokes system with temperature and salinity for free-surface flows

We model free surface flows where density variations coming e.g. from temperature or salinity differences play a significant role. Starting from the compressible Navier-Stokes system, a model is derived by performing the incompressible limit (the dependence of the density on the pressure is removed). A layer-averaged formulation of the model is proposed. The layer-averaged model satisfies a dissipative energy balance. A numerical scheme is proposed. It verifies several stability properties (positivity, well-balancing, maximum principle on the density). Numerical simulations are performed. The differences with models relying on the classical Boussinesq approximation are shown.

Various analytical solutions for the incompressible Euler and Navier-Stokes systems with free surface

In this paper [24], we propose several time dependent analytical solutions for the incompressible Euler and Navier-Stokes systems with free surface. The given analytical solutions concerns the hydrostatic and nonhydrostatic Euler and Navier-Stokes systems.