Section: New Results

Numerical models and simulations applied to physics

Heat and mass transfer in soil and prehistoric fires

Participant : Édouard Canot.

This work is done in the context of the Arphymat project, in collaboration with Archeosciences, IPR and Lebanese International University (LIU), Lebanon.

This work is published in a journal [16] .

This paper is devoted to the simulation of water forced evaporation in a porous saturated medium in a 3D-axisymmetric domain by resolution of partial differential algebraic equations (PDAE) that are encountered in different engineering applications. The goal of this paper is an attempt to present effective realizations, in order to determine the minimal duration of burning for prehistoric occupations. This multidisciplinary work includes scientists in Mathematics, Physics and Archaeology. The model proposed here couples the heat conduction in a water saturated soil with the water steam flow in the medium. We propose an efficient and robust global numerical method, based on a method of lines and differential algebraic equations (DAE) solvers, combined with a Newton method using a powerful sparse linear solver. After a brief overview of classes for numerical techniques applied for moving boundary problems, the Apparent Heat Capacity method (AHC) is used, and in order to validate our codes, a comparison with experiments is done.

Recent work concerns the optimal choice of the temperature interval across which the phase change occurs in the apparent capacity method, because we have to make a compromise between the smoothness of the solution and its accuracy.

Rheology of granular systems flowing out of silo

Participant : Édouard Canot.

This work is done in the framework of a project funded by the Region Bretagne. A PhD thesis (Merline Djouwe-Tankeo), coadvised with Patrick Richard, who is from the Physics Institute at the University of Rennes (IPR), started in February 2009 and will be defended in January 2012.

It has been presented at a conference [36] and a paper is submitted.

We first studied the granular flows by the "discrete elements" method in silo geometries. By changing the micro-mechanical properties of the grains (restitution and friction), we showed that they had a significant influence on the flow discharge. Although models such as "discrete elements" provide access to all the individual properties of the grains, they have one major drawback: the computation time is very important that prohibits the modeling of geophysical and industrial situations. To overcome this problem, we used the "continuous medium" approach, which consider that the granular medium studied follows a rheology recently proposed in the literature. After discussing the numerical implementation, we have studied this rheology for steady and fully developed flows with a semi-analytical method in two configurations: a shear cell and a channel. This allowed us to highlight the differences between a granular medium and a Newtonian fluid.