Benoît Trouette

Transient Rayleigh-Bénard-Marangoni solutal convection

Solutal driven flow is studied for a binary solution submitted to solvent evaporation at the upper free surface. Evaporation induces an increase in the solute concentration close to the free surface and solutal gradients may induce a convective flow driven by buoyancy and/or surface tension. This problem is studied numerically, using several assumptions deduced from previous experiments on polymer solutions. The stability of the system is investigated as a function of the solutal Rayleigh and Marangoni numbers, the evaporative flux and the Schmidt number. The sensitivity of the thresholds to initial perturbations is analyzed. The effect of viscosity variation during drying is also investigated. At last numerical simulations are presented to study the competition between buoyancy and Marangoni effects in the nonlinear regime.

About the ellipticity of the Chebyshev-Gauss-Radau discrete Laplacian with Neumann condition

The Chebyshev-Gauss-Radau discrete version of the polar-diffusion operator, 1r@?@?rr@?@?r-k^2r^2,k being the azimuthal wave number, presents complex conjugate eigenvalues, with negative real parts, when it is associated with a Neumann boundary condition imposed at r=1. It is shown that this ellipticity marginal violation of the original continuous problem is genuine and not due to some round-off error amplification. This situation, which does not lead per se to any particular computational difficulty, is taken here as an opportunity to numerically check the sensitivity of the quoted ellipticity to slight changes in the mesh. A particular mapping is chosen for that purpose. The impact of this option on the ellipticity and on the numerical accuracy of a computed flow is evaluated.

Hybrid atomistic-continuum multiscale method for fluid flow with density variation in microchannels

The present paper extends the hybrid atomistic-continuum multiscale method developed in Vu et al. (2016) to the study of gas flow problems in long microchannels involving density variations. The simulation domain is decomposed into three regions: the bulk where the continuous Navier-Stokes and energy equations are solved, the neighbourhood of the wall simulated by the Molecular Dynamics and the overlap region which connects the macroscopic variables (density, velocity and temperature) between the two former regions. For the simulation of long micro/nano-channels, a strategy with multiple molecular blocks all along the fluid/solid interface is adopted to capture accurately the macroscopic velocity and temperature variations. The validity of the hybrid method is shown by comparisons with a simplified analytical model in the molecular region. Applications to compressible and condensation problems are also presented and the results are discussed. The hybrid method proposed in this paper allows us a cost-effective computer simulations of large scales problems with an accurate modelling of the transfers at small scales (velocity slip, temperature jump, thin condensation films, ...).