A coupling algorithm of the POD–Galerkin method and FVM for heat transfer problems

A novel coupling algorithm of the proper orthogonal decomposition (POD)–Galerkin projection method (PGM) and the finite volume method (FVM) is developed. The proposed coupling algorithm can be easily applied to complex heat transfer problems with a significant reduction in computation time. PGM is only adopted to calculate the sub-domain of heat conduction while FVM is adopted to calculate the sub-domain of the complex flow and heat transfer with openings and turbulence. Moreover, the most critical subject of the coupling of PGM and FVM at the interface based on the interfacial physical variables is comprehensively analyzed. Two coupling strategies are tested and analyzed: (1) D–D (Dirichlet–Dirichlet): the temperature profile at the interface is selected as the transferred information; and (2) D–N (Dirichlet–Neumann): the temperature and the heat flux at the interface are selected as the transferred information. A two-dimensional temperature simulation for an insulated gate bipolar transistor (IGBT) module is selected to assess the performance of the proposed coupling method. All the algorithm analyses in this study are performed via a homemade code based on Python. Results suggest that both the above coupling strategies can obtain a continuous temperature field within the maximum deviation of 0.05∘C compared with the pure FVM simulation results on the entire computational domain for the given two-dimensional problem. The coupling algorithm of D–N(a) (PGM provides heat flux boundary for FVM and FVM provides temperature boundary for PGM at the interface) with the additional source term method achieves the best convergence and its calculation time is only about 1/3–2/5 of that required by pure FVM. The proposed coupling algorithm achieves a high level of accuracy and significantly reduces the computational effort, which has important reference value for subsequent research.