Spectral Methods - Part 1: A fast and accurate approach for solving nonlinear diffusive problems

This paper proposes the use of the Spectral method to simulate diffusive moisture transfer through porous materials, which can be strongly nonlinear and can significantly affect sensible and latent heat transfer. An alternative way for computing solutions by considering a separated representation is presented, which can be applied to both linear and nonlinear diffusive problems, considering highly moisture–dependent properties. The Spectral method is compared with the classical implicit Euler and Crank–Nicolson schemes. The results show that the Spectral approach enables to accurately simulate the field of interest. Furthermore, the numerical gains become particularly interesting for nonlinear cases since the proposed method drastically can reduce the computer run time by 99% when compared to the traditional Crank–Nicolson scheme.