An efficient numerical model for liquid water uptake in porous material and its parameter estimation

Ainagul Jumabekova (1) , Julien Berger (1) , Denys Dutykh (2, 3, 4) , Hervé Le Meur (5, 6) , Aurélie Foucquier (7) , Mickaël Pailha (1) , Christophe Ménézo (1)

1 LOCIE - LabOratoire proCédés énergIe bâtimEnt
2 INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques
3 LAMA - Laboratoire de Mathématiques
4 USMB [Université de Savoie] [Université de Chambéry] - Université Savoie Mont Blanc
5 LM-Orsay - Laboratoire de Mathématiques d'Orsay
6 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352
7 CEA, LITEN, Service bâtiment et systèmes thermiques, Le Bourget du Lac, France

The goal of this study is to propose an efficient numerical model for the predictions of capillary adsorption phenomena in a porous material. The Scharfetter-Gummel numerical scheme is proposed to solve an advection-diffusion equation with gravity flux. Its advantages such as accuracy, relaxed stability condition, and reduced computational cost are discussed along with the study of linear and nonlinear cases. The reliability of the numerical model is evaluated by comparing the numerical predictions with experimental observations of liquid uptake in bricks. A parameter estimation problem is solved to adjust the uncertain coefficients of moisture diffusivity and hydraulic conductivity.

Mots clés: parameter estimation problem; water uptake process; porous material; advection-diffusion equation with gravity flux; Scharfetter-Gummel numerical scheme

Domaines: Mécanique des fluides [physics.class-ph]; Dynamique des Fluides [physics.flu-dyn]; Physique Numérique [physics.comp-ph]; Physique Classique [physics.class-ph]; Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Analyse numérique [cs.NA]; Milieux fluides et réactifs; Thermique [physics.class-ph]

Ainagul Jumabekova, Julien Berger, Denys Dutykh, Hervé Le Meur, Aurélie Foucquier, et al.. An efficient numerical model for liquid water uptake in porous material and its parameter estimation. Numerical Heat Transfer, Part A Applications, 2019, 75 (2), pp.110-136. ⟨10.1080/10407782.2018.1562739⟩. ⟨hal-02047087⟩