A Full Three-Dimensional GPU-Accelerated Model for Deep Borehole Heat Exchangers (DBHEs) Enabling Simulation of Well Arrays

Abstract

Deep borehole heat exchangers (DBHEs) present significant computational challenges due to their multi-scale geometry and long operational timescales. We present a GPU-accelerated three-dimensional model that makes well array simulations computationally tractable through an operator splitting strategy tailored to the problem's physics. The method separates vertical diffusion (stabilized explicit Runge–Kutta–Chebyshev), horizontal diffusion (alternating direction implicit), and advection (semi-Lagrangian), achieving near-unconditional stability with high efficiency. We validate against three published models using different numerical approaches, showing excellent to good agreement. The vendor-agnostic Julia implementation enables full three-dimensional simulation of multi-well arrays on a single GPU, opening new possibilities for systematic design optimization and long-term performance assessment of geothermal well systems. The implementation is released as the open-source Julia package GeothermalWells.jl.