Journal of Porous Media, 22(3):363–385 (2019) EVALUATING MODEL REDUCTION METHODS FOR HEAT AND MASS TRANSFER IN POROUS MATERIALS: PROPER ORTHOGONAL DECOMPOSITION AND PROPER GENERALIZED DECOMPOSITION J. Berger, 1,∗ S. Guernouti, 2 & M. Woloszyn 3 1 Thermal Systems Laboratory, Mechanical Engineering Graduate Program, Pontifical Catholic University of Paraná, Rua Imaculada Conceià ˘ gÃˇ co, 1155, CEP: 80215-901, Curitiba - Paraná, Brazil 2 Cerema, Dter Ouest, Nantes, France 3 Université Savoie Mont Blanc, CNRS, LOCIE, F-73000 Chambéry, France *Address all correspondence to: J. Berger, Thermal Systems Laboratory, Mechanical Engineering Graduate Program, Pontifical Catholic University of Paraná, Rua Imaculada Conceià ˘ gÃˇ co, 1155, CEP: 80215-901, Curitiba - Paraná, Brazil, E-mail: julien.berger@pucpr.edu.br Original Manuscript Submitted: 10/11/2018; Final Draft Received: 10/25/2018 This paper explores deeper the features of model reduction methods proper orthogonal decomposition (POD) and proper generalized decomposition (PGD) applied to heat and moisture transfer in porous materials. The first method is an a posteriori one and therefore requires a previous computation of the solution using the large original model to build the reduced basis. The second one is a priori and does not need any previous computation. The reduced order model is built straightforward. Both methods aim at approaching a high-dimensional model with a low-dimensional one. Their efficiencies, in terms of accuracy, complexity reduction, and CPU time gains, are first discussed on a one-dimensional case of nonlinear coupled heat and mass transfer. The reduced order models compute accurate solutions of the problem when compared to the large original model. They also offer interesting complexity reduction: around 97% for the POD and 88% for the PGD on the case study. In further sections, the robustness of the reduced order models are tested for different boundary conditions and materials. The POD method has lack of accuracy to compute the solution when these parameters differ from the ones used for the learning step. It is also shown that PGD resolution is particularly efficient to reduce the complexity of parametric problems. KEY WORDS: model reduction method, proper generalized decomposition, proper orthogonal decompo- sition, heat and moisture transfer 1. INTRODUCTION Buildings can be affected by damage due to direct or indirect actions of moisture, such as mold growth, corrosion, reduction of thermal resistance of the insulation layers, and so on. The development of damage depends on material properties as well as hygrothermal conditions in construction (Berger et al., 2015a). The latter are governed by heat, air, and moisture balances with the outdoor climate and the indoor conditions, including the impact of factors such as ventilation, internal sources, heating system, and so on. To address these issues of durability, detailed models exist for accurate assessment of heat and mass transfer in building envelopes. To accurately determine the hygrothermal behavior of materials, two- or three-dimensional models can be found in literature for commercial or research uses (Dos Santos and Mendes, 2005, 2009; Hens and Carmeliet, 2002; Kunzel 1091–028X/19/$35.00 © 2019 by Begell House, Inc. www.begellhouse.com 363