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 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.

42 pages, 22 figures, 2 tables, 51 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/

References in corpus (2)

• Finite volume POD-Galerkin stabilised reduced order methods for the parametrised incompressible Navier-Stokes equations
• Stable explicit schemes for simulation of nonlinear moisture transfer in porous materials

Cited by in corpus (5)

• On the comparison of three numerical methods applied to building simulation: finite-differences, RC circuit approximation and a spectral method
• A spectral method for solving heat and moisture transfer through consolidated porous media
• Advanced reduced-order models for moisture diffusion in porous media
• Entanglement control of two-level atoms in dissipative cavities
• Average reduced model to simulate solutions for heat and mass transfer through porous material