An innovative method to determine optimum insulation thickness based on non-uniform adaptive moving grid

  • Suelen GasparinEmail author
  • Julien Berger
  • Denys Dutykh
  • Nathan Mendes
Technical Paper


It is well known that thermal insulation is a leading strategy for reducing energy consumption associated with heating or cooling processes in buildings. Nevertheless, building insulation can generate high expenditures so that the selection of an optimum insulation thickness requires a detailed energy simulation as well as an economic analysis. In this way, the present study proposes an innovative non-uniform adaptive method to determine the optimal insulation thickness of external walls. First, the method is compared with a reference solution to properly understand the features of the method, which can provide high accuracy with less spatial nodes. Then, the adaptive method is used to simulate the transient heat conduction through the building envelope of buildings located in Brazil, where there is a large potential of energy reduction. Simulations have been efficiently carried out for different wall and roof configurations, showing that the innovative method efficiently provides a gain of 25% on the computer run-time.


Optimum insulation thickness Thermal insulation Numerical simulation Moving grid method Redistribution schemes Adaptive numerical methods 

List of symbols

Latin letters


Material specific heat capacity [J/(kg K)]


Energy storage coefficient [J/(m3 K)]


Heat transmission load [MJ/m2]


Convective heat transfer coefficient [W/(m2 K)]


Thermal conductivity [W/(m K)]


Wall length [m]


Heat flux [W/m2]


Temperature [K]


Time [s]


Thickness coordinate direction [m]

Greek letters

\(\alpha \)

Solar absorptivity of outside surface wall

\(\epsilon \)


\(\rho \)

Material density [kg/m3]

\(\sigma \)

Stefan–Boltzmann constant [W/(m2 K4)]

Dimensionless parameters


Biot number

\(c^{\star }\)

Storage coefficient


Fourier number

\(k^{\star }\)

Diffusion coefficient

\(q^{\star }_{\infty }\)

Short-wave radiation source term

\(R_{\text{lw}}^{\star }\)

Long-wave radiation coefficient


Temperature field



This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brasil (CAPES)—in the framework of the International Cooperation Program CAPES/COFECUB (Grant #774/13). The authors also acknowledge the support from CNRS/INSIS and Cellule Énergie under the grant MN4BAT-2017. Professor Mendes thanks the Laboratory LAMA UMR 5127 for the warm hospitality during his visits in 2018, which were supported by the project MN4BAT under the AAP Recherche 2018 Programme of the University Savoie Mont Blanc. Finally, the authors acknowledge the Junior Chair Research program “Building performance assessment, evaluation and enhancement” from the University Savoie Mont Blanc in collaboration with The French Atomic and Alternative Energy Center (CEA) and Scientific and Technical Center for Buildings (CSTB).


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Thermal Systems Laboratory, Mechanical Engineering Graduate ProgramPontifical Catholic University of ParanáCuritibaBrazil
  2. 2.Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, LOCIEChambéryFrance
  3. 3.Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, LAMAChambéryFrance

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