Final result of the project
ATthe end of the project achieved during the semester, the results (on section 5.4) for the benchmark EN 15206 were unsatisfactory, especially for the water content. This problem was due in part to units conversion mistakes, and mainly to an error in the formula of the vapour diffusion \(\delta_\p\). The formula given in [CEN2007] seemed to not be correct. Instead, we used the formula given in [Škerget2014] :
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 imporove the 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
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[CEN2007] EN 15026, Hygrothermal performance of building components and building elements - Assessment of moisture transfer by numerical simulation, CEN, 2007.
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[FeelppMath] Feel++ Mathematics
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[FppPicard] Feel, Non linear problems on http://docs.feelpp.org/math/fem/nonlinear/#_picard_strategy[Feel Mathematics]
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[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
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[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
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[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