We present a topology-based method for mesh-partitioning in three-dimensional discrete fracture network (DFN) simulations that takes advantage of the intrinsic multi-level nature of a DFN. DFN models are used to simulate flow and transport through low-permeability fractured media in the subsurface by explicitly representing fractures as discrete entities. The governing equations for flow and transport are numerically integrated on computational meshes generated on the interconnected fracture networks. Modern high-fidelity DFN simulations require high-performance computing on multiple processors where performance and scalability depends partially on obtaining a high-quality partition of the mesh to balance work-loads and minimize communication across all processors. The discrete structure of a DFN naturally lends itself to various graph representations, which can be thought of as coarse-scale representations of the computational mesh. Using this concept, we develop two applications of the multilevel graph partitioning algorithm to partition the mesh of a DFN. In the first, we project a partition of the graph based on the DFN topology onto the mesh of the DFN and in the second, this DFN-based projection is used as the initial condition for further partitioning refinement of the mesh. We compare the performance of these methods with standard multi-level graph partitioning using graph-based metrics (cut, imbalance, partitioning time), computational-based metrics (FLOPS, iterations, solver time), and total run time. The DFN-based and the mesh-based partitioning methods are comparable in terms of the graph-based metrics, but the time required to obtain the partition is several orders of magnitude faster using the DFN-based partitions. The computation-based metrics show comparable performance between both methods so, in combination, the DFN-based partitions are several orders of magnitude faster than the mesh-based partition. Moreover, the method which uses the DFN-partition solution as the initial condition of the mesh partition provided cut and imbalance values that were close to the mesh-based partition but in a fraction of the time. In turn, this hybrid method outperformed both of the other methods in terms of the total run time.

我们提出了一种基于拓扑的三维离散裂缝网络（DFN）模拟网格划分方法，该方法利用了DFN的固有多级性质。DFN模型用于通过将裂缝明确表示为离散实体来模拟通过地下低渗透性裂缝介质的流动和输送。在相互连接的裂缝网络上生成的计算网格上，将流动和输送的控制方程式进行了数值积分。现代的高保真DFN仿真需要在多个处理器上进行高性能计算，其中性能和可伸缩性部分取决于获得网格的高质量分区以平衡工作负载并最小化所有处理器之间的通信。DFN的离散结构自然适合各种图形表示，可以将其视为计算网格的粗略表示。使用此概念，我们开发了多级图划分算法的两个应用程序来划分DFN的网格。首先，我们将基于DFN拓扑的图分区投影到DFN的网格上，然后，将基于DFN的投影用作进一步划分网格细化的初始条件。我们将这些方法的性能与使用基于图的指标（剪切，不平衡，分区时间），基于计算的指标（FLOPS，迭代，求解器时间）和总运行时间的标准多级图分区进行比较。就基于图形的指标而言，基于DFN的划分方法和基于网格的划分方法是可比的，但是使用基于DFN的划分方法获得划分所需要的时间要快几个数量级。基于计算的指标显示了这两种方法之间可比的性能，因此，结合起来，基于DFN的分区比基于网格的分区要快几个数量级。此外，使用DFN分区解决方案作为网格分区的初始条件的方法提供的剪切和不平衡值接近于基于网格的分区，但时间较短。反过来，就总运行时间而言，此混合方法优于其他两种方法。基于计算的指标显示了这两种方法之间的可比性能，因此，结合起来，基于DFN的分区比基于网格的分区要快几个数量级。此外，使用DFN分区解决方案作为网格分区的初始条件的方法提供的剪切和不平衡值接近于基于网格的分区，但时间较短。反过来，就总运行时间而言，此混合方法优于其他两种方法。基于计算的指标显示了这两种方法之间的可比性能，因此，结合起来，基于DFN的分区比基于网格的分区要快几个数量级。此外，使用DFN分区解决方案作为网格分区的初始条件的方法提供的剪切和不平衡值接近于基于网格的分区，但时间较短。反过来，就总运行时间而言，此混合方法优于其他两种方法。使用DFN分区解决方案作为网格分区的初始条件的方法所提供的剪切和不平衡值接近于基于网格的分区，但时间却很短。反过来，就总运行时间而言，此混合方法优于其他两种方法。使用DFN分区解决方案作为网格分区的初始条件的方法所提供的剪切和不平衡值接近于基于网格的分区，但时间却很短。反过来，就总运行时间而言，此混合方法优于其他两种方法。