  Predictions of physical phenomena in buildings are carried out by using
physical models formulated as a mathematical problem and solved by means of
numerical methods, aiming at evaluating, for instance, the building thermal or
hygrothermal performance by calculating distributions and fluxes of heat and
moisture transfer. Therefore, the choice of the numerical method is crucial
since it is a compromise among (i) the solution accuracy, (ii) the
computational cost to obtain the solution and (iii) the complexity of the
method implementation. An efficient numerical method enables to compute an
accurate solution with a minimum computational run time (CPU). On that account,
this article brings an investigation on the performance of three numerical
methods. The first one is the standard and widely used finite-difference
approach, while the second one is the so-called RC approach, which is a
particular method brought to the building physics area by means of an analogy
of electric circuits. The third numerical method is the spectral one, which has
been recently proposed to solve nonlinear diffusive problems in building
physics. The three methods are evaluated in terms of accuracy on the assessment
of the dependent variable (temperature or vapor pressure) or of density of
fluxes for three different cases: i) heat diffusion through a concrete slab,
ii) moisture diffusion through an aerated concrete slab and iii) heat diffusion
using measured temperatures as boundary conditions. Results highlight the
spectral approach as the most accurate method. The RC based model with a few
number of resistances does not provide accurate results for temperature and
vapor pressure distributions neither to flux densities nor conduction loads.
