Efficient Techniques for Solution of Complex Computational Tasks in Building Physics

Abstract

Various simplification or optimization techniques are sought that reduce demands of computational modeling on time or computing power while keeping a sufficient level of accuracy. In this paper, determination of hygrothermal performance of a brick block is presented using two homogenization techniques based on different principles. While the computational homogenization technique uses a multiscale method realized on the master/slave computer system, the materials homogenization comes out from the effective media theory (EMT), and after the determination of effective material properties, the whole isotropic problem can be transformed to one dimension. Contrary to most applications of EMT, free parameters of mixing formulas are not determined based on an experimental measurement of a single material property but on a complex hygrothermal performance of the element where the distribution of moisture and temperature over a reference year is taken into account. The calculated results from both techniques are compared with results obtained by high-performance computing without any computational simplifications. For materials homogenization, the best results are achieved when k = 0.9 in Lichtenecker’s mixing rule is assumed, which corresponds to a nearly parallel arrangement of the block. The root mean square error (RMSE) of relative humidity (RH) and temperature distribution is only 0.992% and 0.566°C, respectively. This is even better than the results of computational homogenization (RMSE: 1.502% of RH and 0.629°C). Besides obtaining sufficiently precise results, a significant time-saving is achieved, accounting for more than 99%, while being solved on a single-processor computer.