# Stable explicit schemes for simulation of nonlinear moisture transfer in porous materials

Abstract : Implicit schemes have been extensively used in building physics to compute the solution of moisture diffusion problems in porous materials for improving stability conditions. Nevertheless, these schemes require important sub-iterations when treating non-linear problems. To overcome this disadvantage, this paper explores the use of improved explicit schemes, such as Dufort-Frankel, Crank-Nicolson and hyperbolisation approaches. A first case study has been considered with the hypothesis of linear transfer. The Dufort-Frankel, Crank-Nicolson and hyperbolisation schemes were compared to the classical Euler explicit scheme and to a reference solution. Results have shown that the hyperbolisation scheme has a stability condition higher than the standard Courant-Friedrichs-Lewy (CFL) condition. The error of this schemes depends on the parameter \tau representing the hyperbolicity magnitude added into the equation. The Dufort-Frankel scheme has the advantages of being unconditionally stable and is preferable for non-linear transfer, which is the second case study. Results have shown the error is proportional to O(\Delta t). A modified Crank-Nicolson scheme has been proposed in order to avoid sub-iterations to treat the non-linearities at each time step. The main advantages of the Dufort-Frankel scheme are (i) to be twice faster than the Crank-Nicolson approach; (ii) to compute explicitly the solution at each time step; (iii) to be unconditionally stable and (iv) easier to parallelise on high-performance computer systems. Although the approach is unconditionally stable, the choice of the time discretisation $\Delta t$ remains an important issue to accurately represent the physical phenomena.
Keywords :
Type de document :
Pré-publication, Document de travail
35 pages, 16 figures, 1 table, 32 references. Other author's papers can be downloaded at http://w.. 2017
Domaine :
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01404578
Contributeur : Denys Dutykh <>
Soumis le : mardi 28 mars 2017 - 10:21:58
Dernière modification le : jeudi 28 juin 2018 - 12:38:02
Document(s) archivé(s) le : jeudi 29 juin 2017 - 16:28:24

### Fichiers

JB_SG_DD_NM-CFL-2017.pdf
Fichiers produits par l'(les) auteur(s)

### Licence

Distributed under a Creative Commons Paternité - Pas d'utilisation commerciale - Partage selon les Conditions Initiales 4.0 International License

### Identifiants

• HAL Id : hal-01404578, version 4
• ARXIV : 1701.07059

### Citation

Suelen Gasparin, Julien Berger, Denys Dutykh, Nathan Mendes. Stable explicit schemes for simulation of nonlinear moisture transfer in porous materials. 35 pages, 16 figures, 1 table, 32 references. Other author's papers can be downloaded at http://w.. 2017. 〈hal-01404578v4〉

### Métriques

Consultations de la notice

## 709

Téléchargements de fichiers