  The design of numerical tools to model the behavior of building materials is
a challenging task. The crucial point is to save computational cost and
maintain high accuracy of predictions. There are two main limitations on the
time scale choice, which put an obstacle to solve the above issues. First one
is the numerical restriction. A number of research is dedicated to overcome
this limitation and it is shown that it can be relaxed with innovative
numerical schemes. The second one is the physical restriction. It is imposed by
properties of a material, phenomena itself and corresponding boundary
conditions. This work is focused on the study of a methodology that enables to
overcome the physical restriction on the time grid. So-called Average Reduced
Model (ARM) is suggested. It is based on smoothing the time-dependent boundary
conditions. Besides, the approximate solution is decomposed into average and
fluctuating components. The primer is obtained by integrating the equations
over time, whereas the latter is an user-defined empirical model. The
methodology is investigated for both heat diffusion and coupled heat and mass
transfer. It is demonstrated that the signal core of the boundary conditions is
preserved and the physical restriction can be relaxed. The model proved to be
reliable, accurate and efficient also in comparison with the experimental data
of two years. The implementation of the scarce time-step of $1 \, \sf{h}$ is
justified.
  It is shown, that by maintaining the tolerable error it is possible to cut
computational effort up to almost four times in comparison with the complete
model with the same time grid.
