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

The issue to predict the behavior of building materials during wide horizons of time is still challenging. Experimental setups , since they require to perform tests for several years, are costly, never at the full scale and inconvenient. Building Performance Simulation (BPS) programs are designed to perform predictions on computational machines and cut experimental costs significantly. Nonetheless, in the recent review of state-of-the-art, it was indicated that despite the wide range of programs, there are still some drawbacks in terms of the accuracy and the high computational cost. This paper investigates the application of an innovative numerical method, called Super-Time-Stepping (STS) method. It allows performing accurate simulations with time-steps much larger than with standard explicit approaches. These "super" time-steps also enable us to reduce the computational cost. In addition to that, the design of the method allows easier application for models in higher dimensions and with nonlinear parameters. The efficiency of the method is tested on linear and nonlinear academic cases. Further study for the reliability of the model is performed on an experimental case study. The experiment has been carried out on a rammed earth wall during almost 14 months. Obtained data is presented in this article and implemented into proposed model. As a result of the case studies, it is shown that in comparison to the EULER explicit method, the STS methods can cut costs by more than five times while maintaining high accuracy and efficiency. A very fine analysis of the physical phenomena is also performed.

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“…For the sake of clarity, the so-called global heat storage coefficient c T W • s/(m 3 • K) is introduced as in [36]:…”

Section: Governing Equationsmentioning

confidence: 99%

Critical assessment of efficient numerical methods for a long-term simulation of heat and moisture transfer in porous materials

Abdykarim

Berger

Dutykh

et al. 2019

International Journal of Thermal Sciences

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“…In this context, the initial boundary value problem Eq. ( 5) is semi-discretized along the time line [9]. The time discretization parameter is denoted by ∆t , corresponding to the time step of coupling between the numerical models of the co-simulation.…”

Section: The Related Boundary Value Problem In the Context Of Co-simulationmentioning

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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“…The moisture transfer is driven by vapor and liquid diffusions. According to [12,23], the mathematical model to represent the energy and mass conservation in a building porous material can be formulated as follows:…”

Section: Heat and Moisture Balancementioning

confidence: 99%

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

Berger

Busser

Colinart

et al. 2020

International Journal of Thermal Sciences

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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.

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

Cited by 15 publications

References 44 publications

Critical assessment of efficient numerical methods for a long-term simulation of heat and moisture transfer in porous materials

Critical assessment of efficient numerical methods for a long-term simulation of heat and moisture transfer in porous materials

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

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

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