# Final result of the project

In the end of the project made during the semester, the results (on section 5.4) for the benchmark EN 15206 were not correct, especially for the water content. This problem was due to small mistakes of conversion of unities, but mainly because of the formula of the vapour diffusion $\delta_\p$ which was not correct in [CEN2007]. The good formula is [Škerget2014] :

$\delta_\p = \frac{M_w}{RT_\mathrm{ref}}\frac{26.1\times10^{-6}}{200} \frac{1-\frac{w}{146}}{0.503\left(1-\frac{w}{146}\right)^2+0.497}$

Actually : $R_{\mathrm{H}_2 \mathrm{O}}=\frac{R}{M_w}$, where $R$ is the gas constant ($R=8.314\text{J}\,\text{K}^{-1}\text{mol}^{-1}$).

The final results are shown on the page of the case.

## Picard loop

In the project, we also introduced the Picard loop [FppPicard], aiming to have a better solution. On this figure, representing the results after 7 days of simulation, we can see that the results obtained are very similar with and without the Picard loop.

## References

• [CEN2007] EN 15026, Hygrothermal performance of building components and building elements - Assessment of moisture transfer by numerical simulation, CEN, 2007.

• [FeelppMath] Feel++ Mathematics

• [FppPicard] Feel, Non linear problems on http://docs.feelpp.org/math/fem/nonlinear/#_picard_strategy[Feel Mathematics]

• [HDG2020] A HDG method for elliptic problems with integral boundary condition: Theory and Applications, Silvia Bertoluzza, Giovanna Guidoboni, Romain Hild, Daniele Prada, Christophe Prud’homme, R. Sacco, Lorenzo Sala, Marcela Szopos, In progess, 2020

• [Sala2019] Lorenzo Sala. Mathematical modelling and simulation of ocular blood flows and their interactions.Numerical Analysis [math.NA]. Université de Strasbourg, 2019. English. NNT: 2019STRAD021 . tel-02284233v2

• [Škerget2014] Škerget, L. Tadeu, A., BEM numerical simulation of coupled heat, air and moisture flow through a porous solid, Engineering Analysis with Boundary Elements, 2014, 40, p154-161