Building Simulation

, Volume 11, Issue 3, pp 465–481 | Cite as

An improved explicit scheme for whole-building hygrothermal simulation

  • Suelen Gasparin
  • Julien Berger
  • Denys Dutykh
  • Nathan Mendes
Research Article Building Thermal, Lighting, and Acoustics Modeling


Implicit schemes require important sub-iterations when dealing with highly nonlinear problems such as the combined heat and moisture transfer through porous building elements. The computational cost rises significantly when the whole-building is simulated, especially when there is important coupling among the building elements themselves with neighbouring zones and with HVAC (heating ventilation and air conditioning) systems. On the other hand, the classical Euler explicit scheme is generally not used because its stability condition imposes very fine time discretisation. Hence, this paper explores the use of an improved explicit approach—the DuFort–Frankel scheme—to overcome the disadvantage of the classical explicit one and to bring benefits that cannot be obtained by implicit methods. The DuFort–Frankel approach is first compared to the classical Euler implicit and explicit schemes to compute the solution of nonlinear heat and moisture transfer through porous materials. Then, the analysis of the DuFort–Frankel unconditionally stable explicit scheme is extended to the coupled heat and moisture balances on the scale of a one- and a two-zone building models. The DuFort–Frankel scheme has the benefits of being unconditionally stable, second-order accurate in time O(Δt2) and to compute explicitly the solution at each time step, avoiding costly sub-iterations. This approach may reduce the computational cost by twenty as well as it may enable perfect synchronism for whole-building simulation and co-simulation.


heat and moisture transfer numerical methods finite-differences explicit schemes DuFort–Frankel scheme whole-building simulation 


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The authors acknowledge the Brazilian Agencies CAPES of the Ministry of Education and CNPQ of the Ministry of Science, Technology and Innovation, for the financial support.

Supplementary material

12273_2017_419_MOESM1_ESM.pdf (145 kb)
Appendix A. The Dufort-Frankel scheme for weakly coupled equations


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Copyright information

© Tsinghua University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  • Suelen Gasparin
    • 1
    • 3
  • Julien Berger
    • 2
  • Denys Dutykh
    • 3
  • Nathan Mendes
    • 1
  1. 1.Thermal Systems Laboratory, Mechanical Engineering Graduate ProgramPontifical Catholic University of ParanáCuritibaBrazil
  2. 2.Université Savoie Mont Blanc, CNRS, LOCIEChambéryFrance
  3. 3.LAMA, UMR 5127 CNRSUniversité Savoie Mont Blanc, Campus ScientifiqueLe Bourget-du-Lac CedexFrance

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