K. Abahri, R. Bennacer, and R. Belarbi, Sensitivity analyses of convective and diffusive driving potentials on combined heat air and mass transfer in hygroscopic materials, Numerical Heat Transfer, Part A: Applications, vol.69, issue.10, pp.1079-1091, 2005.
URL : https://hal.archives-ouvertes.fr/hal-01711190

H. Anr-project, Vers une méthode de conception HYGRO-thermique des BATiments performants, vol.27, p.32, 2014.

C. Belleudy, A. Kayello, M. Woloszyn, and H. Ge, Experimental and numerical investigations of the effects of air leakage on temperature and moisture fields in porous insulation, Building and Environment, vol.94, p.30, 2015.

C. Belleudy, M. Woloszyn, M. Chhay, and M. Cosnier, A 2D model for coupled heat, air, and moisture transfer through porous media in contact with air channels, Int. J. Heat Mass Transfer, vol.95, pp.453-465, 2005.
DOI : 10.1016/j.ijheatmasstransfer.2015.12.030
URL : https://hal.archives-ouvertes.fr/hal-01815586

J. Berger, S. Gasparin, D. Dutykh, and N. Mendes, Accurate numerical simulation of moisture front in porous material, Building and Environment, vol.118, p.35, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01419018

J. Berger, S. Gasparin, D. Dutykh, and N. Mendes, On the Solution of Coupled Heat and Moisture Transport in Porous Material, Transport in Porous Media, vol.121, issue.3, p.35, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01770386

J. Berger, S. Guernouti, M. Woloszyn, and C. Buhe, Factors governing the development of moisture disorders for integration into building performance simulation, J. Building Eng, vol.3, issue.5, pp.1-15, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01819340

J. Chollom and Z. Jackiewicz, Construction of two-step Runge-Kutta methods with large regions of absolute stability, J. Comp. Appl. Math, vol.157, issue.1, p.24, 2003.

V. P. De-freitas, V. Abrantes, and P. Crausse, Moisture migration in building walls -Analysis of the interface phenomena, Building and Environment, vol.31, issue.2, p.40, 1996.

T. Z. Desta, J. Langmans, and S. Roels, Experimental data set for validation of heat, air and moisture transport models of building envelopes, Building and Environment, vol.46, issue.5, pp.1038-1046, 2005.

G. H. Santos and N. Mendes, Heat, air and moisture transfer through hollow porous blocks, Int. J. Heat Mass Transfer, vol.52, issue.9, pp.2390-2398, 2009.

T. A. Driscoll, N. Hale, and L. N. Trefethen, Chebfun Guide, vol.22, p.25, 2014.

E. C. Dufort and S. P. Frankel, Stability Conditions in the Numerical Treatment of Parabolic Differential Equations. Mathematical Tables and Other Aids to Computation, vol.7, p.18, 1953.

S. Gasparin, J. Berger, D. Dutykh, and N. Mendes, An adaptive simulation of nonlinear heat and moisture transfer as a boundary value problem, International Journal of Thermal Sciences, vol.133, p.35, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02021293

S. Gasparin, J. Berger, D. Dutykh, and N. Mendes, An improved explicit scheme for wholebuilding hygrothermal simulation, Building Simulation, vol.11, issue.3, pp.465-481, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01495737

S. Gasparin, J. Berger, D. Dutykh, and N. Mendes, Stable explicit schemes for simulation of nonlinear moisture transfer in porous materials, J. Building Perf. Simul, vol.11, issue.2, p.19, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01404578

L. Gosse, Computing Qualitatively Correct Approximations of Balance Laws: ExponentialFit, Well-Balanced and Asymptotic-Preserving, SIMAI Springer Series, vol.2, p.15, 2013.

L. Gosse, Viscous equations treated with L-splines and Steklov-Poincare operator in two dimensions, vol.6, p.15, 2017.

L. Gosse, L-Splines and Viscosity Limits for Well-Balanced Schemes Acting on Linear Parabolic Equations, Acta Applicandae Mathematicae, vol.153, issue.1, p.38, 1920.

A. S. Guimaraes, J. M. Delgado, A. C. Azevedo, and V. P. De-freitas, Interface influence on moisture transport in buildings, Construction and Building Materials, vol.162, p.40, 2013.

C. Hagentoft, A. S. Kalagasidis, B. Adl-zarrabi, S. Roels, J. Carmeliet et al., Assessment Method of Numerical Prediction Models for Combined Heat, Air and Moisture Transfer in Building Components: Benchmarks for One-dimensional, Cases. J. Building Phys, vol.27, issue.4, p.40, 2004.

P. D. Hill, Kernel estimation of a distribution function, Communications in StatisticsTheory and Methods, vol.14, issue.3, pp.605-620, 1929.

A. C. Hindmarsh, P. N. Brown, K. E. Grant, S. L. Lee, R. Serban et al., SUNDIALS. ACM Transactions on Mathematical Software, vol.31, issue.3, pp.363-396, 2005.

Z. Jackiewicz, R. Renaut, and A. Feldstein, Two-Step Runge-Kutta Methods. SIAM J. Num. Anal, vol.28, issue.4, p.17, 1991.

S. O. Jensen, Commission of the European Communities: Directorate-General for Science, Research, and Development, p.27, 1986.

T. Kalamees and J. Kurnitski, Moisture Convection Performance of External Walls and Roofs, Journal of Building Physics, vol.33, issue.3, p.5, 2010.

A. C. Khanduri, T. Stathopoulos, and C. Bédard, Wind-induced interference effects on buildings -a review of the state-of-the-art, Engineering Structures, vol.20, issue.7, pp.617-630, 1998.

H. O. Kreiss and G. Scherer, Method of lines for hyperbolic equations, SIAM Journal on Numerical Analysis, vol.29, p.18, 1992.

H. M. Kuenzel and J. Kiessl, Simultaneous heat and moisture transport in building components: one-and two-dimensional calculation using simple parameters, IRB Verlag, issue.10, 1995.

J. Langmans, A. Nicolai, R. Klein, and S. Roels, A quasi-steady state implementation of air convection in a transient heat and moisture building component model, Building and Environment, vol.58, pp.208-218, 2005.

A. V. Luikov, Heat and mass transfer in capillary-porous bodies, vol.10, p.32, 1966.
DOI : 10.1016/s0065-2717(08)70098-4

N. Mendes, M. Chhay, J. Berger, and D. Dutykh, Numerical methods for diffusion phenomena in building physics, PUCPRess, issue.5, 2017.
DOI : 10.7213/978868324455

F. Mnasri, K. Abahri, G. El, R. Bennacer, and S. Gabsi, Numerical analysis of heat, air, and moisture transfers in a wooden building material, Thermal Science, vol.21, issue.2, pp.785-795, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01684849

H. Rafidiarison, R. Rémond, and E. Mougel, Dataset for validating 1-D heat and mass transfer models within building walls with hygroscopic materials, Building and Environment, vol.89, pp.356-368, 1928.
DOI : 10.1016/j.buildenv.2015.03.008
URL : https://hal.archives-ouvertes.fr/hal-01598447

S. Rouchier, T. Busser, M. Pailha, A. Piot, and M. Woloszyn, Hygric characterization of wood fiber insulation under uncertainty with dynamic measurements and Markov Chain Monte-Carlo algorithm, Building and Environment, vol.114, p.32, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01437146

D. L. Scharfetter and H. K. Gummel, Large-signal analysis of a silicon Read diode oscillator, IEEE Transactions on Electron Devices, vol.16, issue.1, p.15, 1969.

, Sensirion. Digital Humidity Sensor, vol.7, p.27, 2019.

G. Söderlind and L. Wang, Evaluating numerical ODE/DAE methods, algorithms and software, J. Comp. Appl. Math, vol.185, issue.2, pp.244-260, 1921.

L. Soudani, A. Fabbri, J. Morel, M. Woloszyn, P. Chabriac et al., Assessment of the validity of some common assumptions in hygrothermal modeling of earth based materials, Energy and Buildings, vol.116, p.10, 2016.

F. Tariku, K. Kumaran, and P. Fazio, Transient model for coupled heat, air and moisture transfer through multilayered porous media, Int. J. Heat Mass Transfer, vol.53, p.10, 2010.
DOI : 10.1016/j.ijheatmasstransfer.2010.03.024

P. J. Taylor, The stability of the Du Fort-Frankel method for the diffusion equation with boundary conditions involving space derivatives, The Computer Journal, vol.13, issue.1, pp.92-97, 1970.

O. Vololonirina, M. Coutand, and B. Perrin, Characterization of hygrothermal properties of wood-based products -Impact of moisture content and temperature, Construction and Building Materials, vol.63, pp.223-233, 1928.
URL : https://hal.archives-ouvertes.fr/hal-01850786

L. Wang and H. Ge, Effect of air leakage on the hygrothermal performance of highly insulated wood frame walls: Comparison of air leakage modelling methods, Building and Environment, vol.123, pp.363-377, 2005.

S. Whitaker, Flow in porous media I: A theoretical derivation of Darcy's law, Transport in Porous Media, vol.1, issue.1, pp.3-25, 1986.

S. Whitaker, Flow in porous media II: The governing equations for immiscible, two-phase flow, Transport in Porous Media, vol.1, issue.2, pp.105-125, 1986.

M. Woloszyn, N. L. Pierrès, Y. Kedowidé, J. Virgone, A. Trabelsi et al., Vers une méthode de conception HYGRO-thermique des BATiments performants : démarche du projet HYGRO-BAT, IBPSA France, vol.27, p.32, 2014.

J. Berger, , p.73000

F. Chambéry and L. , Campus Scientifique, F-73376

D. Dutykh, , p.73000

F. Chambéry, L. Cnrs, U. Savoie-mont, and . Blanc, E-mail address: Denys.Dutykh@univ-smb, Nathan.Mendes@pucpr.edu.br URL, pp.80215-901

B. Rysbaiuly,