A consistent linearization scheme for KGD problems using fracture tip asymptotic solutions

Recently, a fluid volume enrichment strategy based on the asymptotic solutions near crack tip was proposed for fluid-driven fracture propagation problems. Despite its successes in various benchmark and field-scale problems of hydraulic fracturing simulations, aforementioned has following limitations. First, tightly coupled solid-fluid nonlinear system cannot be consistently linearized due to fast marching method applied solve Eikonal equation tracking. As result, an approximated Jacobian had deployed Newton-Raphson iterations. This is particularly troublesome when front propagates into newly fractured cells, since large number iterations are required convergence because inconsistent linearization. Second, existing only focused viscosity-dominated regime. Even though extension toughness-dominated regime could relatively straightforward, it not immediately clear how apply technique transition work dedicated address above two Specifically, unified criterion proposed, which works regime, but also between. The techniques linearize properly initialize primary unknowns demonstrated, result significant reduction convergence. demonstrated context Khristianovic-Geertsma-de Klerk (KGD) relative simplicity.