A spectral method for solving heat and moisture transfer through consolidated porous media

Suelen Gasparin (1, 2) , Denys Dutykh (1, 3, 4) , Nathan Mendes (2)

1 LAMA - Laboratoire de Mathématiques
2 PUCPR - Pontifical Catholic University of Paraná
3 INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques
4 USMB [Université de Savoie] [Université de Chambéry] - Université Savoie Mont Blanc

This work presents an efficient numerical method based on spectral expansions for simulation of heat and moisture diffusive transfers through multilayered porous materials. Traditionally, by using the finite-difference approach, the problem is discretized in time and space domains (Method of lines) to obtain a large system of coupled Ordinary Differential Equations (ODEs), which is computationally expensive. To avoid such a cost, this paper proposes a reduced-order method that is faster and accurate, using a much smaller system of ODEs. To demonstrate the benefits of this approach, tree case studies are presented. The first one considers nonlinear heat and moisture transfer through one material layer. The second case - highly nonlinear - imposes a high moisture content gradient - simulating a rain like condition - over a two-layered domain, while the last one compares the numerical prediction against experimental data for validation purposes. Results show how the nonlinearities and the interface between materials are easily and naturally treated with the spectral reduced-order method. Concerning the reliability part, predictions show a good agreement with experimental results, which confirm robustness, calculation efficiency and high accuracy of the proposed approach for predicting the coupled heat and moisture transfer through porous materials.

Mots clés: Tau-Galerkin method; Spectral methods; numerical simulation; heat and moisture transfer; reduced-order modeling; Chebyshev polynomials

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

Suelen Gasparin, Denys Dutykh, Nathan Mendes. A spectral method for solving heat and moisture transfer through consolidated porous media. International Journal for Numerical Methods in Engineering, 2019, 117 (11), pp.1143-1170. ⟨10.1002/nme.5994⟩. ⟨hal-02023462⟩