A new model for simulating heat, air and moisture transport in porous building materials

Dutykh

Mendes

et al. 2020

Engineering Reports

Self Cite

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.

Section: Resultsmentioning

confidence: 99%

Section: Formulation Of the Mathematical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Dutykh

Mendes

et al. 2020

Engineering Reports

Self Cite

“…where σ total are the total uncertainties regarding the temperature and the vapour pressure fields. The detailed computation of the measurement uncertainties can be verified in [3]. For the temperature evolution, the highest difference is when the relative humidity at the left boundary change from 40 % to 70 % .…”

Section: Comparison Of the Numerical Predictions With Experimental Datamentioning

confidence: 95%

An adaptive simulation of nonlinear heat and moisture transfer as a boundary value problem

Gasparin

International Journal of Thermal Sciences

Dutykh

et al. 2018

Self Cite

An adaptive simulation of nonlinear heat and moisture transfer as a boundary value problem arXiv.org / hal Abstract. This work presents an alternative view on the numerical simulation of diffusion processes applied to the heat and moisture transfer through porous building materials. Traditionally, by using the finite-difference approach, the discretization follows the Method Of Lines (MOL), when the problem is first discretized in space to obtain a large system of coupled Ordinary Differential Equations (ODEs). Thus, this paper proposes to change this viewpoint. First, we discretize in time to obtain a small system of coupled ODEs, which means instead of having a Cauchy (Initial Value) Problem (IVP), we have a Boundary Value Problem (BVP). Fortunately, BVPs can be solved efficiently today using adaptive collocation methods of high order. To demonstrate the benefits of this new approach, three case studies are presented, in which one of them is compared with experimental data. The first one considers nonlinear heat and moisture transfer through one material layer while the second one considers two material layers. Results show how the nonlinearities and the interface between materials are easily treated, by reasonably using a fourth-order adaptive method. Finally, the last case study compares numerical results with experimental measurements, showing a good agreement.Key words and phrases: coupled heat and moisture diffusive transfer; boundary value problems; semi-discretization in time; semi-discretization in space; bvp4c MSC: [2010] 35R30 (primary), 35K05, 80A20, 65M32 (secondary)

“…As discussed and thoroughly motivated in [24][25][26], it is of capital importance to obtain a dimensionless problem before elaborating a numerical model. For this, dimensionless fields are defined:…”

Section: Dimensionless Problemmentioning

confidence: 99%

Critical assessment of a new mathematical model for hysteresis effects on heat and mass transfer in porous building material

International Journal of Thermal Sciences

Busser

Colinart

et al. 2020

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The reliability of mathematical models for heat and mass transfer in building porous material is of capital importance. A reliable model permits to carry predictions of the physical phenomenon with sufficient confidence in the results. Among the physical phenomena, the hysteresis effects on moisture sorption and moisture capacity need to be integrated in the mathematical model of transfer. This article proposes to explore the use of an smooth Bang-Bang model to simulate the hysteresis effects coupled with heat and mass transfer in porous material. This model adds two supplementary differential equations to the two classical ones for heat and mass transfer. The solution of these equations ensures smooth transitions between the main sorption and desorption curves. Two parameters are required to control the speed of transition through the intermediary curves. After the mathematical description of the model, an efficient numerical model is proposed to compute the fields with accuracy and reduced computational efforts. It is based on the Du Fort-Frankel scheme for the heat and mass balance equations. For the hysteresis numerical model, an innovative implicit-explicit approach is proposed. Then, the predictions of the numerical model are compared with experimental observations from literature for two case studies. The first one corresponds to a slow cycle of adsorption and desorption while the second is based on a fast cycling case with alternative increase and decrease of moisture content. The comparisons highlight a very satisfactory agreement between the numerical predictions and the observations. In the last Section, the reliability and efficiency of the proposed model is investigated for long term simulation cases. The importance of considering hysteresis effects in the reliability of the predictions are enhanced by comparison with classical approaches from literature.