The propagation of cracks driven by a pressurized fluid emerges in several areas of engineering, including structural, geotechnical, and petroleum engineering. We present a robust numerical framework to simulate fluid-driven fracture propagation that addresses the challenges emerging in the simulation of this complex coupled nonlinear hydro-mechanical response. We observe that the numerical difficulties stem from the strong nonlinearities present in the fluid equations as well as those associated with crack propagation, from the quasi-static nature of the problem, and from the a priori unknown and potentially intricate crack geometries that may arise. An additional challenge is the need for large scale simulation owing to the mesh resolution requirements and the expected 3D character of the problem in practical applications. To address these challenges we model crack propagation with a high-order hybrid discontinuous Galerkin / cohesive zone model framework, which has proven massive scalability properties, and we model the lubrication flow inside the propagating cracks using continuous finite elements, furnishing a fully-coupled discretization of the solid and fluid equations. The parallel approach for solving the linearized coupled problem consists of standard iterative solvers based on domain decomposition. The resulting computational approach provides the ability to conduct highly-resolved and quasi-static simulations of fluid-driven fracture propagation with unspecified crack path. We conduct a series of numerical tests to verify the computational framework against known analytical solutions in the toughness and viscosity dominated regimes and we demonstrate its performance in terms of robustness and parallel scalability, enabling simulations of several million degrees of freedom on hundreds of processors.

中文翻译：

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在并行计算机上大规模模拟流体驱动裂缝扩展的全耦合计算框架

由加压流体驱动的裂缝扩展出现在多个工程领域，包括结构、岩土和石油工程。我们提出了一个强大的数值框架来模拟流体驱动的裂缝扩展，以解决在模拟这种复杂的耦合非线性流体力学响应中出现的挑战。我们观察到数值困难源于流体方程中存在的强非线性以及与裂纹扩展相关的非线性、问题的准静态性质以及可能出现的先验未知和潜在复杂的裂纹几何形状。另一个挑战是由于网格分辨率要求和实际应用中问题的预期 3D 特征，需要进行大规模模拟。为了应对这些挑战，我们使用高阶混合不连续伽辽金/内聚区模型框架对裂纹扩展进行建模，该框架已证明具有大规模的可扩展性，并且我们使用连续有限元对扩展裂纹内的润滑流进行建模，提供完全耦合的离散化固体和流体方程。解决线性耦合问题的并行方法包括基于域分解的标准迭代求解器。由此产生的计算方法提供了对具有未指定裂纹路径的流体驱动裂缝扩展进行高分辨率和准静态模拟的能力。