  This work presents an alternative view on the numerical simulation of
diffusion processes applied to the heat and moisture transfer through porous
building materials. Traditionally, by using the finite-difference approach, the
discretization follows the Method Of Lines (MOL), when the problem is first
discretized in space to obtain a large system of coupled Ordinary Differential
Equations (ODEs). Thus, this paper proposes to change this viewpoint. First, we
discretize in time to obtain a small system of coupled ODEs, which means
instead of having a Cauchy (Initial Value) Problem (IVP), we have a Boundary
Value Problem (BVP). Fortunately, BVPs can be solved efficiently today using
adaptive collocation methods of high order. To demonstrate the benefits of this
new approach, three case studies are presented, in which one of them is
compared with experimental data. The first one considers nonlinear heat and
moisture transfer through one material layer while the second one considers two
material layers. Results show how the nonlinearities and the interface between
materials are easily treated, by reasonably using a fourth-order adaptive
method. Finally, the last case study compares numerical results with
experimental measurements, showing a good agreement.
