Fluid-driven fracture propagation is widely observed in various geological processes and crucial to many applications of geological engineering. Developing robust and accurate numerical strategies has significance in advancing the scientific understanding and engineering applications related with fluid-driven fracture propagation. We present a finite element-finite volume strategy using asymptotic fracture tip enrichment to model the fluid-driven fracture propagation in three-dimensional Cartesian meshes under the viscosity-dominated regime, in which the fluid viscosity-related process is the dominant energy dissipation mechanism. We use the finite element method to discretize the balance of linear momentum equation for the deformed solid and the finite volume method to discretize the Reynolds equation that governs the fluid flow. In order to track the evolving fracture front in heterogeneous media, we extend the implicit level set approach originally proposed for the displacement discontinuity method. Through this process, a signed distance-based fracture propagation criterion naturally emerges and is suitable for the viscosity-dominated regime when solid toughness becomes irrelevant. Critically, we enrich the fluid volume treatment near the fracture front using the tip asymptotic solution. This enrichment strategy is crucial to overcome the mesh nonconformity caused by the arbitrary intersections between propagating fracture front and underlying Cartesian meshes. We compare the numerical results with analytical solutions of the KGD problem and the penny-shape problem, and illustrate the mesh size and time step-insensitivity of the numerical results due to the tip enrichment technique. Also, we demonstrate the capabilities of the proposed method to model fluid-driven fracture propagation in various heterogeneous media.

中文翻译：

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一种稳健的有限元有限体积策略，用于使用渐近尖端富集的粘度主导的水力裂缝扩展

流体驱动的裂缝扩展在各种地质过程中被广泛观察，对地质工程的许多应用至关重要。开发稳健和准确的数值策略对于促进与流体驱动裂缝扩展相关的科学理解和工程应用具有重要意义。我们提出了一种有限元-有限体积策略，使用渐近裂缝尖端富集来模拟流体驱动的裂缝在三维笛卡尔网格中的扩展，其中流体粘度相关过程是主要的能量耗散机制。我们使用有限元方法对变形固体的平衡线性动量方程进行离散化，并使用有限体积法对控制流体流动的雷诺方程进行离散化。为了跟踪异质介质中不断变化的裂缝前沿，我们扩展了最初为位移不连续方法提出的隐式水平集方法。通过这个过程，一个基于符号距离的断裂扩展准则自然出现，并且适用于当固体韧性变得无关紧要时的粘度主导状态。至关重要的是，我们使用尖端渐近解丰富了裂缝前沿附近的流体体积处理。这种富集策略对于克服由扩展裂缝前沿和下面的笛卡尔网格之间的任意相交引起的网格不整合至关重要。我们将数值结果与 KGD 问题和便士形状问题的解析解进行比较，并说明由于尖端富集技术导致的数值结果的网格尺寸和时间步长不敏感性。此外，我们展示了所提出的方法在各种非均质介质中模拟流体驱动的裂缝扩展的能力。