An explicit algorithm for modeling planar 3D hydraulic fracture growth based on a super-time-stepping method

• DOI: 10.1016/j.ijsolstr.2020.01.011
• Publication Date: 2020-01-15T00:03:03Z
• Authors: Ming Chen; Shicheng Zhang; Sihai Li; Xinfang Ma; Xi Zhang; Yushi Zou
• Keywords: Time stepping

Abstract Hydraulic fracture propagation is a coupled solid-fluid problem involving moving boundaries. The boundary element method is an efficient way to model it in elastic media; however, the computational efficiency is still not promising because in most models the time-consuming implicit approach is used for iteratively solving the stiff equation of the targeted problem. In this paper, we present an explicit super-time-stepping algorithm based on the Runge–Kutta–Legendre method, to simulate a planar 3D hydraulic fracture propagation through the intermediately previous solutions. Each super-time-step covers s stages of single explicit time-step and the results generated can be around s2 times more stable than that using a single explicit time-step. Moreover, an adaptive super-time-step scheme is proposed to capture the marching fracture fronts based on the fracture growth rate. The modeling results are validated against analytical solutions for a penny-shaped hydraulic fracture and experimental results considering stress contrasts. Compared to the implicit iteration approach for the stiff equation, the explicit super-time-stepping algorithm can be up to 30 times faster because of no iteration and super-time-step. Finally, numerical examples are examined for fracture growth in rock formations with stress contrasts and anisotropic toughness, and all the results indicate that the explicit super-time-stepping algorithm can be a promising alternative to the implicit method.