hc_buckleyleverett

Companion code for Efficient design of continuation methods for hyperbolic transport problems in porous media.

A collection of modules and run-scripts for analysing and designing homotopy continuation (HC) methods applied to the Buckley-Leverett problem. Includes:

• An implicit finite-volume discretisation of the 1D Buckley-Leverett problem
• Newton and HC solvers
• Three homotopy strategies (diffusion-based, convex-hull flux, linear relative permeability)
• Homotopy curve traceability analysis via curvature and Newton convergence evaluation

Installation & Reproducing Results

Local setup (requires Python 3.12+):

git clone https://github.com/pschultzendorff/hc_buckleyleverett
cd hc_buckleyleverett
pip install -e .
python hc_buckleyleverett/scripts/buckley_leverett/viscous.py

Docker:

git clone https://github.com/pschultzendorff/hc_buckleyleverett
cd hc_buckleyleverett
docker compose up

Results are saved to hc_buckleyleverett/results/viscous/.

References

If you use this code, please cite:

von Schultzendorff, P.; Both, J.W.; Nordbotten, J.M.; Sandve, T.H. Efficient design of continuation methods for hyperbolic transport problems in porous media. https://arxiv.org/abs/2603.10730

Used references

• Brown, D.A. and Zingg, D.W. (2017). Design and evaluation of homotopies for efficient and robust continuation. Applied Numerical Mathematics, 118, 150-181. https://doi.org/10.1016/j.apnum.2017.03.001
• Brown, D.A. and Zingg, D.W. (2017). Efficient numerical differentiation of implicitly-defined curves for sparse systems. Journal of Computational and Applied Mathematics, 304, 138–159. https://doi.org/10.1016/j.cam.2016.03.002
• Jiang, J., & Tchelepi, H. A. (2018). Dissipation-based continuation method for multiphase flow in heterogeneous porous media. Journal of Computational Physics, 375, 307–336. https://doi.org/10.1016/j.jcp.2018.08.044
• von Schultzendorff, P.; Both, J.W.; Nordbotten, J.M.; Sandve, T.H.; Vohralík, M. Adaptive homotopy continuation solver for incompressible two-phase flow in porous media (in preparation).

Dependencies

jax, matplotlib, seaborn, scikit-image, tqdm, PyQt6

Dev: pytest, mypy, ruff

AI disclosure

Generative AI (GitHub Copilot in VS Code with Claude Opus 4.6) was used to assist with speeding up hc_analysis.hessian_tensor and hc_analysis.HCAnalysisMixin.convergence_metric as well as writing documentation, tests, and type hinting.