## 1 Introduction
They concluded that the roof slope has a more significant influence on the thermal performance of a PCM roof compared to the melting temperature and latent heat of PCM in the region of northeast China. [PERSON] developed a one-dimensional model based on the first law of thermodynamics to carry out the time-dependent simulation of a PCM roof in Istanbul under summer conditions [12]. The results demonstrated that a PCM thickness of 2 cm is suitable for use in flat roofs in this specific area and their experimental and numerical results were consistent. [PERSON] analyzed the thermal performance of a PCM-filled double glazing roof using a numerical method [13]. It was indicated that the semi-transparent property and zenith angle had a big effect on the thermal performance. In addition, the temperature lag time of a PCM roof increases withthe increment of the PCM layer thickness. Although a lot of research related to PCM inserted into a building envelope exists, little work has been carried out for the hot summer and cold winter region in China where the climate conditions are quite different from other areas. In China's hot summer and cold winter region, an air conditioner is indispensable for both the summer cooling season and the winter heating season, which consumes a huge amount of electricity. Based on this, the current paper aims to investigate the conjugate phase change heat transfer and the energy saving benefit in the PCM roof of the hot summer and cold winter region in China. During the past two decades, the lattice Boltzmann method (LBM) has been developed as a powerful numerical method for solving complicated heat transfer problems [14; 15]. For the solid-liquid phase change phenomenon, the existing LBM schemes could be classified into three categories: (1) The phase-field method [16; 17]; (2) the immersed boundary method [18]; (3) the enthalpy-based method [19; 20; 21; 22; 23; 24]. Due to its simplicity and numerical robustness, the enthalpy-based method is the most widely used scheme for simulating solidification and melting problems in scientific and engineering fields. [PERSON] firstly investigated the solid-liquid phase change problem using an enthalpy-based lattice Boltzmann method [19]. However, the iteration of latent heat source term is required in their scheme, which increases the computational load. [PERSON] developed an implicit LBM scheme for conduction with a solid-liquid phase change [20]. By solving a linear system of equations, the numerical iteration process for the latent heat source term could be avoided. To further improve the computational efficiency, [PERSON] modified the equilibrium function for temperature for which the circumstances for the iteration of the latent heat source or solving a linear system of equations are not indispensable [21]. In order to ameliorate the numerical stability and reduce the numerical diffusion during the phase change, [PERSON] further developed the multiple-relaxation-time (MRT) LBM for a solid-liquid phase change using enthalpy formulation [22]. Besides, by decoupling the thermal conductivity and the specific heat from the relaxation time and the equilibrium distribution function, this model is demonstrated to be appropriate for modelling the conjugate heat transfer. Recently, [PERSON] also developed MRT LBM models for axisymmetric and three-dimensional solid-liquid phase change problems [23; 24]. On the other hand, due to its highly parallel nature, the lattice Boltzmann method has been successfully installed into graphics processor units (GPU) to achieve parallel computing for several different heat transfer and fluid flow applications [25; 26; 27; 28; 29; 30]. In this paper, the MRT enthalpy-based LBM with GPU acceleration was used to investigate the conjugate phase change heat transfer of a PCM roof in the hot summer and cold winter region of China.