Section: New Results

Complex fluids

Participant : Sébastien Boyaval.

The aim of the research performed in the project-team about complex fluids is mainly focused on the mathematical modelling and numerical simulation of i) non-Newtonian rheologies, with application to geophysical fluids such as mudflows, or the solid transport in rivers, and ii) stratified flows, in particular free-surface flows, which naturally occur in the geophysical context under gravity influence.

The need for reduced models is crucial for numerical computations at the large geophysical scale. S. Boyaval has therefore pursued his research about a systematic asymptotic reduction technique for thin-layers of non-Netwonian fluids with a near hydrostatic pressure [11] . On the other hand, accurate numerical simulations (for benchmark purposes at least) require a full 3D model mainly based on Stokes-like equations, and there is a constant need for better computation methods in that field too. With a view to condensed high-order approximations of elliptic PDEs like the Stokes equation on generic meshes (obtained by refinement or agglomeration of a simplicial initial mesh), S. Boyaval has participated in a joint work about hybridization of a mixed-dual generic approach [8] . On the hydraulic applications side, the studies initiated at CEMRACS 2013 about a stochastic representation of fluctuations in the transport of river sediments by bed-load have been published [9] .