A spectral method for solving heat and moisture transfer through consolidated porous media

Gasparin, Suelen; Dutykh, Denys; Mendes, Nathan

doi:10.1002/nme.5994

Cited by 8 publications

(6 citation statements)

References 47 publications

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“…It aims in building a reduced-order model (ROM). Several approaches are used in the literature [12,22] and the Proper Orthogonal Decomposition (POD) is one of the most used and widely known. Interested readers are invited to consult [46][47][48][49][50] a primary overview.…”

Section: Pod Reduced-order Model With Time Reduced Basismentioning

confidence: 99%

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Assessing the wall energy efficiency design under climate change using POD reduced order model

Berger,

Allery,

Machard

2022

Preprint

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Within the environmental context, numerical modeling is a promising approach to assess the energy efficiency of building. Resilient buildings need to be designed, capable of adapting to future extreme heat. Simulations are required assuming a one-dimensional heat transfer problem through walls and a simulation horizon of several years (nearly 30). The computational cost associated with such modeling is quite significant and model reduction methods are worth investigating. The objective is to propose a reliable reduced-order model for such long-term simulations. For this, an alternative model reduction approach is investigated, assuming a known Proper Orthogonal Decomposition reduced basis for time, and not for space as usually. The model enables computing parametric solutions using basis interpolation on the tangent space of the Grassmann manifold. Three study cases are considered to verify the efficiency of the reduced-order model. Results highlight that the model has a satisfying accuracy of 10 −3 compared to reference solutions. The last case study focuses on the wall energy efficiency design under climate change according to a four-dimensional parameter space. The latter is composed of the load material emissivity, heat capacity, thermal conductivity and thickness insulation layer. Simulations are carried over 30 years considering climate change. The solution minimizing the wall work rate is determined with a computational ratio of 0.1% compared to standard approaches.

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Section: Pod Reduced-order Model With Time Reduced Basismentioning

confidence: 99%

“…In [20,21], the Proper Generalized Decomposition (PGD) is used to compute the heat and mass transfer in porous walls for one and two-dimensional problems. A Spectral reduced method is employed to solve similar problems in [10,22]. The well-known Proper Orthogonal Decomposition (POD) is also used in [23,24].…”

Section: Introductionmentioning

confidence: 99%

Assessing the wall energy efficiency design under climate change using POD reduced order model

Berger,

Allery,

Machard

2022

Preprint

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“…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].…”

Section: Introductionmentioning

confidence: 99%

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

Azam

Berger

Guernouti

et al. 2021

Journal of Building Performance Simulation

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Estimating the temperature field of a building envelope could be a time-consuming task. The use of a reduced-order method is then proposed: the Proper Generalized Decomposition method. The solution of the transient heat equation is then re-written as a function of its parameters: the boundary conditions, the initial condition, etc. To avoid a tremendous number of parameters, the initial condition is parameterized. This is usually done by using the Proper Orthogonal Decomposition method to provide an optimal basis. Building this basis requires data and a learning strategy. As an alternative, the use of orthogonal polynomials (Chebyshev, Legendre) is here proposed.

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“…It is still an open challenge to propose efficient numerical models that reduce computational costs and maximize the accuracy of the solution. Some recent works presented innovative approaches such as boundary element methods, super‐time‐stepping approach, or reduced order models . However, the air transfer is neglected in these works.…”

Section: Introductionmentioning

confidence: 99%

“…Some recent works presented innovative approaches such as boundary element methods, 17 super-time-stepping approach, 18 or reduced order models. 19,20 However, the air transfer is neglected in these works. Thus, these investigations only deal with systems of diffusion equations.…”

Section: Introductionmentioning

confidence: 99%

An efficient numerical model for the simulation of coupled heat, air, and moisture transfer in porous media

Berger

Dutykh

Mendes

et al. 2020

Engineering Reports

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This article proposes an efficient explicit numerical model with a relaxed stability condition for the simulation of heat, air, and moisture transfer in porous material. Three innovative approaches are combined to solve the system of two differential advection‐diffusion equations coupled with a purely diffusive equation. First, the DU FORT‐FRANKEL scheme is used to solve the diffusion equation, providing an explicit scheme with an extended stability region. Then, the two advection‐diffusion equations are solved using both the SCHARFETTER‐GUMMEL numerical scheme for the space discretisation and the two‐step RUNGE‐KUTTA method for the time variable. This combination enables to relax the stability condition by one order. The proposed numerical model is evaluated on three case studies. The first one considers quasi‐linear coefficients. The theoretical results of the numerical schemes are confirmed by our computations. Indeed, the stability condition is relaxed by a factor of 40 compared to the standard EULER explicit approach. The second case provides an analytical solution for a weakly nonlinear problem. A very satisfactory accuracy is observed between the reference solution and the one provided by the numerical model. The last case study assumes a more realistic application with nonlinear coefficients and ROBIN‐type boundary conditions. The computational time is reduced 10 times by using the proposed model in comparison with the explicit EULER method.

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A spectral method for solving heat and moisture transfer through consolidated porous media

Cited by 8 publications

References 47 publications

Assessing the wall energy efficiency design under climate change using POD reduced order model

Assessing the wall energy efficiency design under climate change using POD reduced order model

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

An efficient numerical model for the simulation of coupled heat, air, and moisture transfer in porous media

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