Acceleration methods for the planar 3D ILSA hydraulic fracturing model
Abstract
Planar 3D models of hydraulic fracturing provide a practical balance between models with restrictive geometric assumptions and fully 3D simulators, capturing fractures with arbitrary planar footprints at moderate computational cost. Nevertheless, applications such as treatment design optimization and mini-frac test interpretation require large ensembles of simulations, for which the cost of planar 3D models remains a significant bottleneck. This work presents acceleration strategies for the planar 3D Implicit Level Set Algorithm (ILSA) to reduce simulation runtime while preserving numerical accuracy. A unified planar 3D ILSA scheme that consolidates the nested loops of the elastohydrodynamic solver and the front tracking algorithm into a single iterative process is introduced. A matrix splitting approach is applied to the linearized elastohydrodynamic system, moving the dense part of the elasticity operator to the right-hand side and yielding a sparse system matrix that can be solved more efficiently. Anderson acceleration is incorporated into the solution of the elastohydrodynamic system to improve convergence. A predictor--corrector scheme is additionally examined in combination with these methods. Each technique is evaluated individually and in combination on both the reference and unified schemes across five benchmark cases. Numerical experiments demonstrate that the unified scheme alone delivers an average 2.3x speed-up, reaching 3.8x for the Sandglass case. The combined application of all techniques achieves an average 4.2x speed-up and up to 14.4x for the Sandglass case. The schemes are also assessed during fracture closure, where the matrix splitting and Anderson acceleration prove most effective, together reaching up to 3.4x.
Versions
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BibTeX
@misc{shukalo2026acceleration,
title = {{Acceleration methods for the planar 3D ILSA hydraulic fracturing model}},
author = {V. I. Shukalo and A. V. Valov and A. N. Baykin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.20025},
eprint = {2606.20025},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.20025},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Acceleration methods for the planar 3D ILSA hydraulic fracturing model
AU - V. I. Shukalo
AU - A. V. Valov
AU - A. N. Baykin
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2606.20025
UR - https://arxiv.org/abs/2606.20025
AB - Planar 3D models of hydraulic fracturing provide a practical balance between models with restrictive geometric assumptions and fully 3D simulators, capturing fractures with arbitrary planar footprints at moderate computational cost. Nevertheless, applications such as treatment design optimization and mini-frac test interpretation require large ensembles of simulations, for which the cost of planar 3D models remains a significant bottleneck. This work presents acceleration strategies for the planar 3D Implicit Level Set Algorithm (ILSA) to reduce simulation runtime while preserving numerical accuracy. A unified planar 3D ILSA scheme that consolidates the nested loops of the elastohydrodynamic solver and the front tracking algorithm into a single iterative process is introduced. A matrix splitting approach is applied to the linearized elastohydrodynamic system, moving the dense part of the elasticity operator to the right-hand side and yielding a sparse system matrix that can be solved more efficiently. Anderson acceleration is incorporated into the solution of the elastohydrodynamic system to improve convergence. A predictor--corrector scheme is additionally examined in combination with these methods. Each technique is evaluated individually and in combination on both the reference and unified schemes across five benchmark cases. Numerical experiments demonstrate that the unified scheme alone delivers an average 2.3x speed-up, reaching 3.8x for the Sandglass case. The combined application of all techniques achieves an average 4.2x speed-up and up to 14.4x for the Sandglass case. The schemes are also assessed during fracture closure, where the matrix splitting and Anderson acceleration prove most effective, together reaching up to 3.4x.
ER -