An Order 102 Speedup in the Computation of the Steady-State Thermal Response of Geothermal Heat Exchangers

The long-term thermal response of geothermal heat exchangers plays a fundamental role in their correct sizing. A possible approach is to approximate that long-term behaviour by a time-periodic one, in which an infinite series of harmonic terms is superposed to a steady-state component. While for the harmonic terms analytical expressions are known, the steady-state component must be obtained numerically. In the present work the use of an iterative, and matrix-free, solver combined with a preconditioner derived from the very physics of the problem is presented, which compared to a sparse direct solver leads to an order 10(2) speedup in the computation of the steady-state thermal response of geothermal heat exchangers.