Abstract
We introduce a partitioned coupling approach for iterative coupling of flow processes in deformable fractures embedded in a poro-elastic medium that is enhanced by interface quasi-Newton (IQN) methods. In this scope, a unique computational decomposition into a fracture flow and a poro-elastic domain is developed, where communication and numerical coupling of the individual solvers are realized by consulting the open-source library preCICE. The underlying physical problem is introduced by a brief derivation of the governing equations and interface conditions of fracture flow and poro-elastic domain followed by a detailed discussion of the partitioned coupling scheme. We evaluate the proposed implementation and undertake a convergence study to compare a classical interface quasi-Newton inverse least-squares (IQN-ILS) with the more advanced interface quasi-Newton inverse multi-vector Jacobian (IQN-IMVJ) method. These coupling approaches are verified for an academic test case before the generality of the proposed strategy is demonstrated by simulations of two complex fracture networks. In contrast to the development of specific solvers, we promote the simplicity and computational efficiency of the proposed partitioned coupling approach using preCICE and FEniCS for parallel computations of hydro-mechanical processes in complex, three-dimensional fracture networks.
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Acknowledgments
Holger Steeb and Patrick Schmidt gratefully acknowledge the funding provided by the German Federal Ministry of Education and Research (BMBF) for the GeomInt (I & II) project (Grant Numbers 03A0004E and 03G0899E) in the BMBF Geoscientific Research Program “Geo:N Geosciences for Sustainability”. Alexander Jaust, Miriam Schulte, and Holger Steeb thank the German Research Foundation (DFG) for supporting this work under Grant No. SFB 1313 (Project No. 327154368). We thank the preCICE developers for their support, especially B. Uekermann.
Funding
Open Access funding enabled and organized by Projekt DEAL. Holger Steeb and Patrick Schmidt gratefully acknowledge the funding provided by the German Federal Ministry of Education and Research (BMBF) for the GeomInt (I & II) project (Grant Numbers 03A0004E and 03G0899E) in the BMBF Geoscientific Research Program “Geo:N Geosciences for Sustainability”. Alexander Jaust, Miriam Schulte, and Holger Steeb thank the DFG for supporting this work under Grant No. SFB 1313 (Project No. 327154368).
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Schmidt, P., Jaust, A., Steeb, H. et al. Simulation of flow in deformable fractures using a quasi-Newton based partitioned coupling approach. Comput Geosci 26, 381–400 (2022). https://doi.org/10.1007/s10596-021-10120-8
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DOI: https://doi.org/10.1007/s10596-021-10120-8
Keywords
- Fracture flow
- Hydro-mechanics
- Hybrid-dimensional modeling
- Partitioned coupling
- Quasi-Newton methods
- preCICE
Mathematics Subject Classification (2010)
- 76S05
- 74F10
- 90C53