## Section: New Software and Platforms

### Heat diffusion in soils

#### HeMaTiS

Participants : Édouard Canot [correspondant] , Salwa Mansour.

HeMaTiS (**He**at and **Ma**ss **T**ransfer **i**n **S**oils) is a
set of Finite Volume programs (variants concern different geometrical
configurations: 1D, 1D-radial, 2D, 3D-axisymmetric) for computing the
transient heat diffusion in soils when there is a phase change of water.
Currently, the soil is modelled by a heterogeneous porous medium having
constant thermo-physical properties, and the porous medium is
saturated with water. The phase change is treated by means of the Apparent
Heat Capacity method. In the near future, we plan to use an unsaturated
model (but limited to small water content), and an effective thermal
conductivity which depends on the local humidity (this latter law may
reveal hysteresis behaviour). The software is written in Fortran 95 and
is based on the Muesli library (
5.3.2 ). A Computer Algebra System
(Maple or Maxima) is used to compute the Jacobian matrix.

#### TPIP

Participants : Édouard Canot [correspondant] , Salwa Mansour.

TPIP (**T**hermal **P**roperties by **I**nverse **P**roblem) is a program
which aims at estimating the thermo-physical of a saturated porous medium
after a strong heating which leads to the phase change of the water contained
in the pores, knowing the experimental heating curves history at few selected
points. The least-square criterion is used, in which sensitivity coefficients
are the solution of a huge, complex PDE system in order to take into account
the phase change of water. These equations for the sensitivity coefficients
are therefore obtained via a Computer Algebra System (Maple or Maxima).
In many aspects, the forward problem is similar to the HeMaTiS code
(
5.4.1 ), and like it, is based on Muesli (
5.3.2 ). Two
different minimization algorithms may be used, Damped Gauss-Newton or
Levenberg-Marquardt. A special procedure has been applied in order to
obtain a robust convergence, by changing some parameters of the forward
problem during the iterations.

#### GLiMuH

Participants : Édouard Canot [correspondant] , Salwa Mansour.

The GLiMuH code (**G**rains with **Li**quid **M**eniscus **u**nder **H**eating) is devoted
to the understanding of how heat diffuses
in an assembly of solid grains separated by air and water. In the
pendular regime, the quantity of water is very small, leading to liquid
bridges between the grains. In the current approximation, the grains
are spherical in shape, and the numerical simulation is done in a 3D
axisymmetric coordinate system. The shape of the liquid/gas interface
is computed by integrating a differential algebraic system of equations,
with a given quantity of water per unit volume of the porous medium,
and under the constraint of a given contact angle between the liquid/gas
interface and the solid boundaries. The numerical results allow us to
estimate the effective thermal conductivity of a real wet granular medium,
which is required to establish more realistic models for the HeMaTiS code
(
5.4.1 ).