A robust finite element‐finite volume strategy for viscosity‐dominated hydraulic fracture propagation using an asymptotic tip enrichment

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