Average reduced model to simulate solutions for heat and mass transfer through porous material

Abstract

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.