Solving nonlinear diffusive problems in buildings by means of a Spectral reduced-order model

Abstract

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 reducedorder 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.

Parametric PGD model used with orthogonal polynomials to assess efficiently the building's envelope thermal performance

“…We investigate here the use of a polynomial basis like Chebyshev or Legendre. Out of the approximation theory [5], those basis have proven to be very efficient at solving partial differential equations using spectral methods [6,7].…”

Hygrothermal performance assessments of traditional timber-framed houses in Turkey by numerical analysis

“…Moisture-based problems have been one of the critical issues as long-term effects on walls in terms of energy efficiency, indoor environmental quality, and durability. Hygrothermal performance has had direct impacts on the users, material durability, and energy efficiency of a building [1]. A well-performing building façade is based on two critical issues: thermal resistance and vapor permeability [2].…”

Average reduced model to simulate solutions for heat and mass transfer through porous material

“…Numerous studies concentrated on evolution, moderation, and replacement of classical numerical approaches. 1,2 The fidelity and the efficiency of a numerical method are crucial for long-term modeling. 3,4 In the recent review of the state-of-the-art, [5][6][7] it was indicated that despite a wide range of programs, there are still some drawbacks in terms of accuracy, ease-of-use, and the high computational cost.…”