Comparative investigation of methods for incorporating real climate data into thermal quadrupoles models: fitting techniques, integral transforms, and inversion algorithms

Solving the heat equation is a necessity in numerous applications, and the methods available for this purpose range from simple analytical resolutions (for a suitable set of assumptions) to more sophisticated numerical ones (complex geometries, non-linear problems...). The thermal quadrupoles 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. The following work concerns the incorporation of climate data recordings of hourly external temperature and solar heat flux in the thermal quadrupoles method for solving the heat equation through a building wall. To allow their transformation into the Laplace domain, the climate data (which exhibit severe fluctuations and peaks) are fitted by means of two techniques, namely, a Fourier series fit and Gaussian-Lorentzian asymmetric lineshapes. The considered problem corresponds to building walls of multiple layer composition. The wall is modelled as a cylinder, allowing a 2D axisymmetric representation in cylindrical coordinates which in turn dictates the need for Hankel transforms for the space domain. Moreover, this application of both time and space transforms while including fitted functions of real climate data raises the question of the proper inversion method to return to the original time-space domain after solving the quadrupole equations. Stehfest, De Hoog and Den Iseger algorithms are therefore investigated. Results of different combinations of the fitting method/inversion algorithm (or a coupling of algorithms) are provided and compared against a finite element resolution of the problem (COMSOL). This work is carried out within the framework of the Resbiobat project funded by the French national research agency (ANR).

Work In Progress