An efficient finite volume model for shallow geothermal systems. Part I: Model formulation

This series of two papers presents a three-dimensional finite volume model for shallow geothermal systems. In this part, an efficient computational model describing heat and fluid flow in ground-source heat pumps is formulated. The physical system is decomposed into two subdomains, one representing a soil mass, and another representing one or a set of borehole heat exchangers. Optimization of the computational procedure has been achieved by, first, using a pseudo three-dimensional line element for modeling the borehole heat exchanger, and second, using a combination of a locally refined Cartesian grid and a multigrid with hierarchal tree data structure for discretizing and solving the soil mass governing equations. This optimization made the model computationally efficient and capable of simulating multiple borehole heat exchangers embedded in a multilayer system, in relatively short CPU time. In Part II of this series, verifications and numerical examples describing the computational capabilities of the model are presented.