Benchmark solution
=====================


Calculation method used for the reference solution
--------------------------------------------------------

The 2 reference solutions are obtained by solving the drying equation by finite differences using Scilab. The command file is given in the appendix in order to be able to possibly test new models.

The spatial discretization is the same as for Aster, namely :math:`1\mathit{mm}` meshes. The time discretization is 3600 seconds for the Mensi equation, and 60 seconds for the Bazant equation.


Benchmark results
----------------------

We are interested in the water concentration in the test tube after 1 hour, 3 days, 28 days, 1.25 years, 3 years and 5 years. The evolution of the profiles obtained with Scilab for Mensi's law and Bazant's law is visible on [:ref:`Figure 2.2-a <Figure 2.2-a>`] and [:ref:`Figure 2.2-b <Figure 2.2-b>`].

**Note:**

The comparison between Scilab and Aster solutions is visible in [:ref:`§Annexe 2 <§Annexe 2>`]: the concentrations obtained in the test tube are shown after 1 hour and after 5 years. The good correlation is thus verified except for the solution obtained with Aster for Mensi's law after one hour where an oscillation is observed which very much suggests a violation of the principle of the maximum observed in thermal energy (cf. [:ref:`bib2 <bib2>`]). It would therefore be interesting to be able to use lumped elements when solving the drying equation even if the phenomenon is accentuated here due to the boundary conditions, since the water concentration is directly imposed instead of imposing a flow [:ref:`bib3 <bib3>`].


.. image:: images/10046C9800003F9A0000384783EA517DC0023D95.svg
    :width: 521
    :height: 460


.. _RefImage_10046C9800003F9A0000384783EA517DC0023D95.svg:


.. _Ref74108946:

**Figure** **2.2-a: Scilab solution - Mensi's law**


.. image:: images/10046C4000003F9A0000384786F40A03315EB3D0.svg
    :width: 521
    :height: 460


.. _RefImage_10046C4000003F9A0000384786F40A03315EB3D0.svg:


.. _Ref74108948:

**Figure** 2.2-a **.2-b: Scilab solution - Bazant's law**

The TEST_RESU are made for the 6 characteristic moments at the abscissa :math:`x\mathrm{=}\mathrm{0mm}`, :math:`x\mathrm{=}40\mathit{mm}` and :math:`x\mathrm{=}60\mathit{mm}`.


Bibliographical references
---------------------------


1. L. GRANGER: "Deferred behavior of concrete in nuclear power plant enclosures" published by the Central Laboratoire des Ponts et Chaussées (1996).


2. S. MICHEL - PONNNELLE, A. RAZAKANAIVO: "Project I7-01-08: Quality of Solid Mechanics Studies — Step No. 4: Finite Element Study", Note EDF: HT‑64/02/007/A, June 2002


3. G. DEBRUYNE, B. CIREE: "Modeling thermohydration, drying and concrete shrinkage", *Code_Aster* Reference Manual, [:ref:`R7.01.12 <R7.01.12>`] (2001).