Towards new numerical models of erosion: from the rheometer to the river, with a detour through the analysis of partial differential equations
The aim of the SEDIFLO project is to propose a new mathematical modeling of physical processes inducing erosion and sedimentation of particles in watercourses, by contributing to the transfer of recent mechanical knowledge towards hydraulic engineering. We seek in particular to model mechanical processes for non-cohesive solid particles (sand, gravels), which involve exchanges of matter between a river and its bed during the dynamic rebalancing of the forces after a forced imbalance (flood, tank hunting). ). <br />At present, the understanding of the physical mechanisms involved in the erosion of a river bed remains very small, essentially empirical. However, important progress seems possible, especially thanks to recent theories in mechanics of dense granular suspensions. In fact, a new modeling, which would better describe macroscopic solid transport phenomena at the river section scale (useful to hydraulic engineers), would therefore allow by extension to improve the digital models of rivers with moving bed that are used by Hydraulic engineers, then improve the prediction of erosion and sedimentation in the watercourse interacting with humans (by simulating improved models). <br />Finally, it should be noted that in anthropogenic activities interacting with watercourses, erosion and sedimentation resulting from them are often at the origin of dangers for humans and nature. However, our ability to predict hazards based on empirical knowledge is challenged after climate change or adaptation. The study proposed by SEDIFLO, of analytical rather than empirical essence, is therefore part of a logic of controlled and sustainable management of rivers.
The work of the SEDIFLO project uses the mathematical analysis of partial differential equations and their numerical simulation to evaluate the relevance of recent theories resulting from the mechanics of dense granular suspensions to model erosion and sedimentation.
In particular, mathematical tools of discretization and reduction of equations will be used to evaluate the physical relevance of (approximate) solutions in increasingly complex configurations approaching river erosion.
New theoretical and numerical results have been obtained for the formulation of mathematical models of free-surface complex flows, which is useful for modeling large-scale erosion (in rivers).
The project currently aims to numerically evaluate new models of complex flows using recent mathematical results to formulate them.
Communications in conferences with acts made it possible to disclose the first mathematical results obtained.
SEDIFLO deals with the mathematical modelling and the numerical simulation of non-cohesive sediment transport in rivers.
Indeed, sediment transport is a crucial environmental process in numerous cross-interactions between human activities and fluvial eco-systems.
The quantitative prediction of the solid mass transported, in particular, is important to understand river morphodynamics as well as to guide river managers.
But although the transport of non-cohesive sediment in rivers is a century-old subject of research,
there is not yet a theory that accurately describes simultaneously physical processes occuring at dilute and dense concentrations of sediments.
In all current approaches, that critical region has been heuristically reduced to a poorly defined ``interface'' in between the bed and the suspension.
Now, this modelling artefact is recognized as unsatisfactory to account for many situations where the surface of the bed evolves in time.
It is specially the case in the flush of a dam.
The main aim of SEDIFLO is to provide one with a comprehensive description of the region where the sediments concentration varies fast,
and thereby, more accurate numerical predictions of sediment transport in rivers.
SEDIFLO strategy is to tackle the problem with a bottom-up approach from the rheology viewpoint,
in view of the recent theoretical and experimental results collected in that field about dense granular suspensions.
Technically, it will also rely on the use of advanced mathematical tools (asymptotic model reduction, and numerical discretization of PDEs)
to transfer rheological innovations from the laboratory scale to the river scale.
The tasks will be divided into two work packages.
A first work package consists in specifying the rheological innovations to the context of rivers at the lab scale.
It will be achieved by a multidisciplinary team centered around a postdoctoral fellow.
The postdoctoral fellow, with aptitudes in theoretical fluid mechanics or mathematical physics, and a little bit of scientific computing,
shall be recruited thanks to the requested ANR grant.
A second work package consists in applying validated mathematical techniques to models of sediment transport in rivers that contain rheology.
A PhD student skilled in analytical and numerical methods for PDEs will be recruited with the requested ANR grant to that aim.
He will be supervised by a team of young applied mathematicians.
The project is both for performing innovative scientific tasks with useful applications,
and an opportunity for consolidating the research project of the coordinator.
The requested ANR grant, mainly for the recruitment of two non-permanent researchers, therefore qualifies for the JCJC funding tool.
Deliverables are mathematical models, and numerical schemes allowing for computer simulations useful in practice (i.e. highly accurate in 3D/2D, and very fast in 2D/1D).
Numerical validations will help at evaluating the results in benchmark test cases at the laboratory and geophysical scales.
SEDIFLO outputs should straightforwardly improve the numerical simulation of the flush event in a dam,
at the same time a compulsory operation to maintain hydropower plants efficient and a big concern for river managers.
We finally recall that originalities of the project are the consortium and the location.
The project covers a broad range of expertise,
and will be hosted in a laboratory commited to produce results useful to the industrial practice of hydraulic engineering:
the Laboratoire d'hydraulique Saint-Venant.
Monsieur Sébastien Boyaval (Laboratoire d'hydraulique Saint-Venant/Ecole Nationale des Ponts et Chaussées)
The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.
ENPC Laboratoire d'hydraulique Saint-Venant/Ecole Nationale des Ponts et Chaussées
Help of the ANR 244,400 euros
Beginning and duration of the scientific project: September 2015 - 48 Months