A non-history dependent temporal superposition algorithm for the finite line source solution

Abstract

Simulations of the operation of fields of borehole heat exchangers involve a wide spectrum of time scales, and hourly simulations for decades are required for the evaluation of the heat transfer in the subsurface due to these systems. Most current models rely on time and space superposition of fundamental analytical solutions of the heat equation to build the solution for complex borehole fields configurations and loading conditions. These procedures are robust and accurate but do not have favorable scaling properties, and the problems can become quickly computationally intractable as the size increases. In this context, acceleration algorithms for temporal superposition are key to overcome this limitation. This paper presents developments on the so-called "non-history dependent" acceleration scheme and its application to the point and line source solutions, which are commonly used as building blocks in borehole field simulations. The results obtained show promising properties as the computational complexity of the proposed algorithm is linear in the number of time steps, and near double precision accuracy can be achieved by refining the discretizations used to compute the integrals arising from the scheme.