  This work presents a detailed mathematical model combined with an innovative
efficient numerical model to predict heat, air and moisture transfer through
porous building materials. The model considers the transient effects of air
transport and its impact on the heat and moisture transfer. The achievement of
the mathematical model is detailed in the continuity of Luikov's work. A system
composed of two advection-diffusion differential equations plus one exclusively
diffusion equation is derived. The main issue to take into account the
transient air transfer arises in the very small characteristic time of the
transfer, implying very fine discretisation. To circumvent these difficulties,
the numerical model is based on the Du Fort-Frankel explicit and
unconditionally stable scheme for the exclusively diffusion equation. It is
combined with a two-step Runge-Kutta scheme in time with the Scharfetter-Gummel
numerical scheme in space for the coupled advection-diffusion equations. At the
end, the numerical model enables to relax the stability condition, and,
therefore, to save important computational efforts. A validation case is
considered to evaluate the efficiency of the model for a nonlinear problem.
Results highlight a very accurate solution computed about 16 times faster than
standard approaches. After this numerical validation, the reliability of the
mathematical model is evaluated by comparing the numerical predictions to
experimental observations. The latter is measured within a multi-layered wall
submitted to a sudden increase of vapor pressure on the inner side and driven
climate boundary conditions on the outer side. A very satisfactory agreement is
noted between the numerical predictions and experimental observations
indicating an overall good reliability of the proposed model.
