An improved explicit scheme for whole-building hygrothermal simulation

Gasparin, Suelen; Berger, Julien; Dutykh, Denys; Mendes, Nathan

doi:10.1007/s12273-017-0419-3

Cited by 21 publications

(25 citation statements)

References 22 publications

(45 reference statements)

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“…Therefore, a parametric study of the EULER explicit scheme is omitted, as it was already discussed in the literature in comparison with DU FORT-FRANKEL scheme. Interested readers may consult these previous results in [26,27]. From Figure 6 one can see that the L ∞ error of the STS methods is high for small values of ∆ t. Basically, the error between two orange dashed lines, show that the STS methods "prefers" time-steps bigger than ∆ t CFL , required for stability of the EULER explicit scheme in accordance with the CFL condition 3.3.…”

Section: Resultsmentioning

confidence: 85%

“…The method was first presented in the listed works [43][44][45] almost 50 years ago. In this article, the detailed discretization of the scheme is omitted, and interested readers can refer to the recent papers [26,27]. There the method has been extended for coupled equations of heat and mass transfer, and its performance has been discussed in more details.…”

Section: The Du Fort-frankel Methodsmentioning

confidence: 99%

“…This condition imposes certain restrictions for the application of the EULER explicit scheme into building simulation tools [27]. Secondly, compared to EULER implicit scheme, the STS methods are much easier to implement, since it has an explicit formulation.…”

Section: The Super-time-stepping Methodsmentioning

confidence: 99%

“…Another improved explicit approach, namely DU FORT-FRANKEL method is used for a critical assessment of the STS method. The method was deeper explored in the works of GASPARIN et al [26,27].…”

Section: Conclusion 1 Introductionmentioning

confidence: 99%

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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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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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Section: Resultsmentioning

confidence: 85%

Section: The Du Fort-frankel Methodsmentioning

confidence: 99%

Section: The Super-time-stepping Methodsmentioning

confidence: 99%

Section: Conclusion 1 Introductionmentioning

confidence: 99%

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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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“…According to the standard VON NEUMANN stability analysis, the DU FORT ‐FRANKEL scheme is unconditionally stable . Further details and examples of applications of this scheme may be consulted in References and .…”

Section: The Numerical Modelmentioning

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 New Stable, Explicit, Third‐Order Method for Diffusion‐Type Problems

Kovács

Nagy

Saleh

2022

Advcd Theory and Sims

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This paper reports on a novel explicit numerical method for the spatially discretized diffusion or heat equation. After discretizing the space variables as in conventional finite difference methods, this method does not use a finite difference approximation for the time derivatives, it instead combines constant-neighbor and linear-neighbor approximations, which decouple the ordinary differential equations, thus they can be solved analytically. In the obtained three-stage method, the time step size appears in exponential form with negative coefficients in the final expression. This property guarantees unconditional stability, as it is shown using von Neumann stability analysis. It is also proved that the convergence of the method is third order in the time step size. After verification, by solving Fisher's and Huxley's equations, it is demonstrated that it works for nonlinear equations as well. The new algorithm is tested against widely used numerical solvers for cases where the media is strongly inhomogeneous. According to the results, the new method is significantly more effective than the traditional explicit or implicit methods, especially for extremely large stiff systems. It is believed that this new method is unique in the sense that it is the first unconditionally stable explicit method with third-order convergence.

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An improved explicit scheme for whole-building hygrothermal simulation

Cited by 21 publications

References 22 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

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

A New Stable, Explicit, Third‐Order Method for Diffusion‐Type Problems

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