An efficient and robust fracture-grid and fracture-fracture intersection detection method for polygon fractures in unstructured polyhedral grids

摘要

Fracture-grid and fracture-fracture intersection detection with non-conforming grids is an important procedure used in fractured medium flow simulations. Recently, unstructured grids have been used extensively because of their high flexibility. This paper presents an efficient and robust method to detect the intersection of polygon fractures in unstructured polyhedral grids. The procedures are divided into two parts: computing intersection points and generating intersection lines and intersection polygons. For the first part, we classified all intersection points into three types; grid-indexed octrees and grid-indexed geometric topologies were used to accelerate the search and computation of intersection points, respectively. For the second part, we discussed all different possible intersection conditions and classified these conditions into two combination patterns by the number of fracture-edge-grid-face intersections. A uniform method is presented to generate intersection polygons in different patterns with good performance; fracture-grid connections are utilized to improve the efficiency of the detection of fracture-fracture intersections. We tested the method using a complex fracture network containing 2000 fractures and 8 cases with different shapes and scales of grids. The performance test results coincide with the algorithm analysis. This method can largely improve the efficiency of intersection detection in fractured medium flow simulations using non-conforming grids.