An Unstructured Moving Element Mesh for Hydraulic Fracture Modeling

A flexible computational method that can be used to represent the complex geometric evolution of a fluid-driven fracture front using an unstructured triangular element mesh has been developed. A specific motivation for the method is to enable the future treatment of nonplanar fracture growth problems. Elastic interactions between the crack opening displacements and the surrounding medium are calculated using displacement discontinuity boundary element influence functions. A novel feature of the approach is the use of an adjustable region of tip elements to accommodate both time-dependent crack edge movements and to ensure correct velocity-dependent asymptotic behavior for viscous and viscous-toughness flow conditions. The adjustable tip element region is represented using a special-purpose data structure that allows the iteration of the moving edge element vertices to be linked directly to the flow rate and the crack opening solution values that are determined in each time step. The fringe region is periodically replaced with a set of fixed vertex elements as the fracture surface evolves. The replacement algorithm also allows for the remeshing of the element grid adjacent to the crack front in cases where the edge advance distance is uneven. The remeshing scheme yields a more uniform mesh size with corresponding benefits in computational performance. The proposed scheme has been evaluated using available analytic and experimental results for planar fracture propagation. The method is found to be both accurate and robust for a range of choices of geometric fracture shapes, time step sizes and edge velocity variations.