Comparative investigation of numerical methods for incorporating real climate data into thermal quadrupole models for building wall applications: fitting techniques, and Laplace inversion algorithms
The thermal quadrupole method provides the advantage of expressing the partial differential formulation of the heat equation as a linear system in transformed time (Laplace transform) and space (integral transforms) domains. It allows faster computations compared to standard techniques such as Finit...
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| Vydané v: | International journal of thermal sciences Ročník 220; s. 110362 |
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| Jazyk: | English |
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Elsevier Masson SAS
01.02.2026
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| Abstract | The thermal quadrupole method provides the advantage of expressing the partial differential formulation of the heat equation as a linear system in transformed time (Laplace transform) and space (integral transforms) domains. It allows faster computations compared to standard techniques such as Finite Element Methods. The following work concerns the incorporation of climate data recordings of hourly external temperature and solar heat flux in the thermal quadrupole method for solving the heat equation through a multilayered building wall. Two methods are proposed for the purpose of applying Laplace transforms to the discrete sets of climate data: a global Fourier series fit, accounting for severe fluctuations and peaks with the number of harmonics depending on dataset size; and a discrete Laplace transform methodology applied to a global series of linearly computed sub-series over defined intervals. Two models are investigated, a 1D heat transfer problem in Cartesian coordinates and a 2D axisymmetric representation in cylindrical coordinates, the latter dictating Hankel transforms for the space domain. After solving in the transformed domains, the challenge lies in accurately retrieving time-domain results. Three Laplace inversion algorithms—Stehfest, De Hoog, and Den Iseger—are investigated for their numerical stability, accuracy, and efficiency. A parametric analysis related to parameters of the data fitting and Laplace inversion methods is carried out. Results of different combinations of the fitting method/inversion algorithm (or a coupling of algorithms) are provided and compared with a finite element resolution of the thermal problems (FreeFEM++ and COMSOL) with an emphasis on computational time enhancements. The main objective of this work is to develop a numerically efficient direct model suitable for future application in inverse methods. |
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| AbstractList | The thermal quadrupole method provides the advantage of expressing the partial differential formulation of the heat equation as a linear system in transformed time (Laplace transform) and space (integral transforms) domains. It allows faster computations compared to standard techniques such as Finite Element Methods. The following work concerns the incorporation of climate data recordings of hourly external temperature and solar heat flux in the thermal quadrupole method for solving the heat equation through a multilayered building wall. Two methods are proposed for the purpose of applying Laplace transforms to the discrete sets of climate data: a global Fourier series fit, accounting for severe fluctuations and peaks with the number of harmonics depending on dataset size; and a discrete Laplace transform methodology applied to a global series of linearly computed sub-series over defined intervals. Two models are investigated, a 1D heat transfer problem in Cartesian coordinates and a 2D axisymmetric representation in cylindrical coordinates, the latter dictating Hankel transforms for the space domain. After solving in the transformed domains, the challenge lies in accurately retrieving time-domain results. Three Laplace inversion algorithms—Stehfest, De Hoog, and Den Iseger—are investigated for their numerical stability, accuracy, and efficiency. A parametric analysis related to parameters of the data fitting and Laplace inversion methods is carried out. Results of different combinations of the fitting method/inversion algorithm (or a coupling of algorithms) are provided and compared with a finite element resolution of the thermal problems (FreeFEM++ and COMSOL) with an emphasis on computational time enhancements. The main objective of this work is to develop a numerically efficient direct model suitable for future application in inverse methods. |
| ArticleNumber | 110362 |
| Author | Ibos, Laurent Zibouche, Kamel Waeytens, Julien Mortada, Mostafa Feuillet, Vincent |
| Author_xml | – sequence: 1 givenname: Mostafa orcidid: 0009-0009-1000-1481 surname: Mortada fullname: Mortada, Mostafa email: mostafa.mortada@u-pec.fr organization: Univ Paris Est Creteil, CERTES, F-94010, Creteil, France – sequence: 2 givenname: Vincent surname: Feuillet fullname: Feuillet, Vincent organization: Univ Paris Est Creteil, CERTES, F-94010, Creteil, France – sequence: 3 givenname: Laurent surname: Ibos fullname: Ibos, Laurent organization: Univ Paris Est Creteil, CERTES, F-94010, Creteil, France – sequence: 4 givenname: Kamel orcidid: 0000-0003-3489-7584 surname: Zibouche fullname: Zibouche, Kamel organization: Centre Scientifique et Technique Du Bâtiment (CSTB), 84 Avenue Jean Jaurès, 77420, Champs-sur-Marne, France – sequence: 5 givenname: Julien orcidid: 0000-0001-8858-7130 surname: Waeytens fullname: Waeytens, Julien organization: Univ Gustave Eiffel, COSYS, IMSE, Cité Descartes, 14-20 Boulevard Newton, 77420, Champs-sur-Marne, France |
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| Cites_doi | 10.1016/j.measurement.2013.02.020 10.1016/j.est.2019.101007 10.1016/j.enbuild.2022.112511 10.1016/j.ijthermalsci.2024.109566 10.1115/1.4002777 10.1016/j.enbuild.2020.110130 10.1016/j.ijthermalsci.2006.11.008 10.1016/j.enbuild.2020.110346 10.1016/j.enbuild.2018.12.002 10.1016/j.eti.2021.101673 10.1016/j.ijthermalsci.2023.108681 10.1016/j.ijthermalsci.2006.05.006 10.1016/j.icheatmasstransfer.2017.11.008 10.1016/j.enbuild.2019.04.042 10.1145/361953.361969 10.1137/0903022 10.1016/j.ijheatmasstransfer.2011.04.020 10.1016/j.ijthermalsci.2024.109463 10.1287/opre.14.3.444 10.1016/j.enbuild.2013.01.011 10.1016/j.enbuild.2022.112166 10.1016/j.ijheatmasstransfer.2017.08.042 10.1017/S0269964806060013 10.1016/j.applthermaleng.2024.124084 10.1016/j.conbuildmat.2024.137773 10.1016/j.icheatmasstransfer.2024.108364 |
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| Keywords | Thermal quadrupoles Computation time Climate data Integral transforms Laplace inversion algorithms Building walls |
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| SubjectTerms | Building walls Climate data Computation time Integral transforms Laplace inversion algorithms Mechanics Physics Thermal quadrupoles Thermics |
| Title | Comparative investigation of numerical methods for incorporating real climate data into thermal quadrupole models for building wall applications: fitting techniques, and Laplace inversion algorithms |
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