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Register a new userSolving nonlinear diffusive problems in buildings by means of a Spectral Reduced-Order Model
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Authors
Suelen Gasparin
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This paper proposes the use of a Spectral method to simulate diffusive moisture transfer through porous materials as a Reduced-Order Model (ROM). The Spectral approach is an a priori method assuming a separated representation of the solution. The method is compared with both classical Euler implicit and Crank-Nicolson schemes, considered as large original models. Their performance - in terms of accuracy, complexity reduction and CPU time reduction - are discussed for linear and nonlinear cases of moisture diffusive transfer through single and multi-layered one-dimensional domains, considering highly moisture-dependent properties. Results show that the Spectral reduced-order model approach enables to simulate accurately the field of interest. Furthermore, numerical gains become particularly interesting for nonlinear cases since the proposed method can drastically reduce the computer run time, by a factor of 100, when compared to the traditional Crank-Nicolson scheme for one-dimensional applications.
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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.
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