Section: New Results

Complex fluids

Participants : Sébastien Boyaval, Dena Kazerani.

The aim of the research performed in the project-team about complex fluids is

• to guide the mathematical modeling with PDEs of multi-phase flowing materials, like liquid suspensions of particles or stratified air-water flows, and

• to propose efficient algorithms for the computation of flow solutions, mainly for the many applications in the hydraulic engineering context.

The analysis of heterogeneous flow models for the paradigmatic complex fluids of Maxwell type has been pursued [38], [34], in particular for gravity flows with a free surface (natural in the hydraulic engineering context). It is planned to pursue the analysis with other fluids, and obtain thereby mathematically-sound models for the erosion of sediment. Dena Kazerani has recently started working on that goal, in the context of the on-going ANR JCJC project SEDIFLO of S. Boyaval with E. Audusse (Paris 13), A. Caboussat (Genève), A. Lemaitre (ENPC) and M. Parisot (Inria ANGE).

Even for Newtonian fluids like water, the simpler models that are currently used do not always produce satisfactory numerical results in the hydraulic engineering context, especially because the data that is used to perform numerical predictions is uncertain. Considering that some model uncertainties induce (stochastic) parametric variations like material heterogeneities, S. Boyaval pursued his analysis of new fast algorithms to compute many PDE solutions for many parameter values in the (uncertain) hydraulic engineering context [30], [54].