This repository contains information and code to reproduce the results presented in the article

@inproceedings{wittenstein2026dbhe,
  author    = {Wittenstein, Collin and Lujan, Emmanuel and Inglis, Andrew and Metcalfe, Robert and Edelman, Alan and Ranocha, Hendrik},
  title     = {A Full Three-Dimensional {GPU}-Accelerated Model for Deep Borehole Heat Exchangers ({DBHEs}) Enabling Simulation of Well Arrays},
  booktitle = {Proceedings of the 51st Stanford Geothermal Workshop},
  year      = {2026},
  address   = {Stanford, California},
  publisher = {Stanford University},
  url       = {https://pangea.stanford.edu/ERE/db/GeoConf/papers/SGW/2026/Wittenstein.pdf}
}

Read the paper

If you find these results useful, please cite the article mentioned above. If you use the implementations provided here, please also cite this repository as

@misc{wittenstein2026dbheRepro,
  title={Reproducibility repository for
         "A Full Three-Dimensional {GPU}-Accelerated Model for Deep Borehole Heat Exchangers ({DBHEs}) Enabling Simulation of Well Arrays"},
  author={Wittenstein, Collin and Lujan, Emmanuel and Inglis, Andrew and Metcalfe, Robert and Edelman, Alan and Ranocha, Hendrik},
  year={2026},
  howpublished={\url{https://github.com/cwittens/2026_DBHEs_Arrays}},
  doi={10.5281/zenodo.18405149}
}

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 (semiLagrangian), 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.

To reproduce the numerical experiments presented in this article, you need to install Julia. See the detailed installation instructions in the code/README.md.

The numerical experiments presented in this article were performed using Julia v1.12.3

First, you need to download this repository, e.g., by cloning it with git or by downloading an archive via the GitHub interface. Then, you need to start Julia in the code directory of this repository and follow the instructions described in the code/README.md file therein.

• Collin Wittenstein (Massachusetts Institute of Technology & Johannes Gutenberg University Mainz)
• Emmanuel Lujan (Massachusetts Institute of Technology)
• Andrew Inglis (Massachusetts Institute of Technology)
• Robert Metcalfe (Massachusetts Institute of Technology)
• Alan Edelman (Massachusetts Institute of Technology)
• Hendrik Ranocha (Johannes Gutenberg University Mainz)

The code in this repository is published under the MIT license, see the LICENSE file.

Everything is provided as is and without warranty. Use at your own risk!