Title: Advanced reduced-order models for moisture diffusion in porous media,
Abstract: It is of great concern to produce numerically efficient methods for moisture
diffusion through porous media, capable of accurately calculate moisture
distribution with a reduced computational effort. In this way, model reduction
methods are promising approaches to bring a solution to this issue since they
do not degrade the physical model and provide a significant reduction of
computational cost. Therefore, this article explores in details the
capabilities of two model-reduction techniques - the Spectral Reduced-Order
Model (Spectral-ROM) and the Proper Generalised Decomposition (PGD) - to
numerically solve moisture diffusive transfer through porous materials. Both
approaches are applied to three different problems to provide clear examples of
the construction and use of these reduced-order models. The methodology of both
approaches is explained extensively so that the article can be used as a
numerical benchmark by anyone interested in building a reduced-order model for
diffusion problems in porous materials. Linear and non-linear unsteady
behaviors of unidimensional moisture diffusion are investigated. The last case
focuses on solving a parametric problem in which the solution depends on space,
time and the diffusivity properties. Results have highlighted that both methods
provide accurate solutions and enable to reduce significantly the order of the
model around ten times lower than the large original model. It also allows an
efficient computation of the physical phenomena with an error lower than
10^{-2} when compared to a reference solution.