Contribution à la modélisation hygrothermique des bâtiments : application des méthodes de réduction de modèle

Abstract : Excessive levels of moisture in buildings may damage the construction quality. Moisture also has an effect on indoor air quality and thermal comfort of the occupants. Thus moisture is a possible source of disorders in buildings. It is therefore important to continue developing numerical models to simulate the global hygrothermal behaviour of buildings. To achieve this aim, it is necessary to solve non-linear problems, with high space and time scales, with fine discretisation and sometimes parametric. This mathematical problems are complex to solve. Thus model reduction techniques and efficient ways of numerical simulation are worth investigations. Two techniques were assessed : the Proper Orthogonal Decomposition (POD) and the Proper Generalised Decomposition (PGD). They were first applied on non-liner coupled heat and mass transfers in porous materials. Both were compared and evaluated carrying about the reduction of the cost of resolution and the precision of the solution computed. Following this analysis, the PGD was selected for our next investigations. Due to it representation, the PGD method has several interesting features, already reviewed in literature.Thus, chapter 3 proposed to illustrate this advantages on different issues of modelling buildings hygrothermal behaviours. We focused on the reduction of the complexity of multi-dimensional problems, on the globalisation of local problems and on building PGD parametric solution or meta-model. Several academic case study were considered to illustrate these points. We analysed non-linear heat and mass transfers in porous materials and multizone air building transfers. In last part, we elaborated a PGD reduced order model to perform whole building energy simulation. Two different models were built. The first one associates a PGD model for envelope problem and a large original model for multizone problem. This work was done during a collaboration with the LST laboratory, at PUCPR University, Curitiba, Brazil. The main interest was the benefits of using their validated and admitted model Domus for solving multizone problem. Two case study were analysed. The first one analyse a parametric problem for the study of the retrofitting a building in function of the vapour permeability of the insulating material. The second one focused on the whole building energy simulation of a two-zone building with 2-dimension transfers in the wall assembly. A second global PGD reduced order model was elaborated, with a higher reduction of the numerical complexity of the problem. This model associates a PGD model for solving envelope problem and a PGD parametric solution for the multizone problem. The performance of this model was analysed investigating the numerical gain and the precision of the solution computed. In conclusion, the relevance of reduction model techniques for performing whole building energy simulation was revealed. The PGD method contributes to a new approach for solving this problems.
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Julien Berger. Contribution à la modélisation hygrothermique des bâtiments : application des méthodes de réduction de modèle. Génie civil. Université de Grenoble, 2014. Français. ⟨NNT : 2014GRENA028⟩. ⟨tel-01127189⟩

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