#### Numerical Simulation of Ground Heat Exchangers Based on Model Order Reduction Method Zhendi Ma, Qiongxiang Kong*, Peifen Wang, Siyan Liu, Liwen Jin

Abstract

The model order reduction (MOR) method is to convert a large system into a small system, which can reduce the amount of data calculation and save time and cost while maintaining a certain precision. In this paper, Krylov subspace, balanced truncation and Laguerre orthogonal polynomial MORs are developed to the numerical simulation of the heat transfer characteristics of ground heat exchangers under laminar and turbulent conditions. Firstly, the finite volume method is used to discretize the two-dimensional governing equation into an ordinary differential equation with respect to the pipe length direction. Then three MOR systems are established respectively. Finally, the specific examples are calculated. The results show that for a certain length of ground heat exchangers the total time taken by the balanced truncation method is much larger than that of the direct solution method, the Krylov subspace method and the Laguerre orthogonal polynomial method. The reasonable orders of the reduced order systems by the Krylov subspace method and the Laguerre orthogonal polynomial method are both 20. At this time, their solving time is all less than 11.3% (laminar flow) and 6.2% (turbulent flow) of the direct solution method. And the relative errors under the above conditions are all less than 10-7. As the length of the calculated pipe increases, the efficiency of the two MOR methods is more prominent.

Keywords model order reduction (MOR), ground heat exchanger, Krylov subspace, Laguerre orthogonal polynomial, balanced truncation