Solving nonlinear diffusive problems in buildings by means of a reduced spectral method

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 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.

Keywords

Bibliographic record

BibTeX Citation

@article{Gasparin2019solvingnonlinear,
  author = {Gasparin, S. and Berger, J. and Dutykh, D. and Mendes, N.},
  title = {Solving nonlinear diffusive problems in buildings by means of a reduced spectral method},
  journal = {J. of Build. Perf. Sim.},
  year = {2019},
  volume = {12},
  number = {1},
  pages = {17--36},
  doi = {10.1080/19401493.2018.1458905},
  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 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.},
  keywords = {reduced-order modelling, Spectral methods, numerical simulation of diffusive phenomena, nonlinear problems, Galerkin method, moisture diffusion, Chebyshev polynomials, building physics}
}