Section: New Results

Numerical models and simulations applied to physics

Small scale modeling of porous media

Participants : Édouard Canot, Salwa Mansour.

Grants: ARPHYMAT 8.4.3 , 8.4.4

Software: GLiMuH 5.4.3

Publications: [22]

Abstract: This study is devoted to the heat transfer between two spherical grains separated by a small gap; dry air is located around the grains and a liquid water meniscus is supposed to be present between them. This problem can be seen as a micro-scale cell of an assembly of solid grains, for which we are looking for the effective thermal conductivity. For a fixed contact angle and according to the volume of the liquid meniscus, two different shapes are possible for the meniscus, giving a “contacting” state (when the liquid makes a true bridge between the two spheres) and a “non-contacting” one (when the liquid is split in two different drops, separated by a thin air layer); the transition between these two states occurs at different times when increasing or decreasing the liquid volume, thus leading to a hysteresis behavior when computing the thermal flux across the domain.

Heat and mass transfer modeling in porous media

Participants : Édouard Canot, Salwa Mansour.

Grants: HYDRINV 8.4.5

Software: HeMaTiS ( 5.4.1 )

Abstract: The physical model of the HeMaTiS code ( 5.4.1 ) has been recently improved by adding the diffusion process of dry air through the water steam which is created by the evaporation of the water inside the porous medium. In this fashion, not only can the heating stage of the surface of the soil be simulated but also the cooling stage. The application concerns the study of archaeological fires which were used many times a day; the possibility of alternation of heating and cooling may lead to a better interpretation of residual marks left in the ground. Work is in progress to validate the numerical results.

Inverse problem for determining the thermo-physical properties of a porous media

Participants : Édouard Canot, Salwa Mansour.

Grants: HYDRINV 8.4.5

Software: TPIP ( 5.4.2 )

Publications: [23]

Abstract: This study concerns the inverse problem which consists of the estimation of thermophysical properties of the soil knowing the temperature at few selected points of the domain. In order to solve this inverse problem, we used the least square criterion where we try to minimize the error function between real measures and simulated ones. The coupled system composed of the energy equation together with the three sensitivity boundary initial problems resulting from differentiating the basic energy equation with respect to the soil properties must be solved. To overcome the stiffness of our problem (due to the use of Apparent Heat Capacity method), the high nonlinearity of the coupled system and the problem of large residuals we used the Damped Gauss Newton and Levenberg-Marquardt methods. Moreover, we emphasized on the importance of the choice of $\Delta T$ (temperature range over which the phase change occurs) where for a certain initial guess the inverse problem fails to converge. We overcome this problem by chaining the inverse problems using different values of $\Delta T$ and parameters’ set.

Geodesy

Participant : Bernard Philippe.

Grants: LIRIMA-EPIC 8.4.2 .

Publications: [12] .

Abstract: We solve a geodetic inverse problem for the determination of a distribution of point masses (characterized by their intensities and positions), such that the potential generated by them best approximates a given potential field.