Section: Application Domains

Fluids with complex rheology

Whereas the viscous effects can often be neglected in water flows, they have to be taken into account in situations such as avalanches, debris flows, pyroclastic flows, erosion processes,...i.e. when the fluid rheology becomes more complex. Gravity driven granular flows consist of solid particles commonly mixed with an interstitial lighter fluid (liquid or gas) that may interact with the grains and decrease the intensity of their contacts, thus reducing energy dissipation and favoring propagation. Examples include subaerial or subaqueous rock avalanches (e.g. landslides).

As mentioned above, the main issue is to propose models of reduced complexity, suitable for scientific computing and endowed with stability properties (continuous and/or discrete). In addition, models and their numerical approximations have to be confronted with experimental data, as analytical solutions are hardly accessible for these problems/models. A. Mangeney (IPGP) and N. Goutal (EDF) may provide useful data.

Arbitrary topography

Most shallow water type models are derived under the assumption of small/ smooth bottom variations whereas in practice the topography along which the flow (avalanche, debris flow,...) occurs can be quite steep and rough. An improved Saint-Venant system, due to Savage-Hutter, and valid for large slopes and small slope variations has been proposed. A new model relaxing all restrictions upon the topography has been proposed for shallow water flows by Bouchut et al. [24] , [27] . The extension of this work to the case of models with distributed velocities along the vertical axis is an important objective with many applications (landslides, avalanches,...).

Erosion and sedimentation

The sediment transport modelling is of major interest in terms of applications. It also raises interesting issues from a numerical aspect. This is an example of coupling between the flow and another phenomenon, namely the deformation of the bottom of the basin that can be carried out either by bed load where the sediment has its own velocity or suspended load in which the particles are mostly driven by the flow. This phenomenon involves different time scales and nonlinear retroactions; hence the need for accurate mechanical models and very robust numerical methods. In collaboration with industrial partners (EDF–LNHE), the team already works on the improvement of numerical methods for existing (mostly empirical) models but our aim is also to propose new (quite) simple models that contain important features and satisfy some basic mechanical requirements. The extension of our 3D models to the transport of weighted particles can also be here of great interest.