A Novel Approach for Direct Numerical Simulation of Hydraulic Fracture Problems

Hydraulic fracturing is a non-linear and multi-physics problem involving the break up of a solid medium due to the action of hydrodynamic forces. Fluid and solid mechanics are involved at the same time together with fracture mechanics. Despite its relevance in many scientific and engineering fields, the theoretical and numerical description of hydraulic fracturing remains a challenging matter and the capabilities of existing models for applications are still limited. In this context, we propose a novel numerical approach to the Direct Numerical Simulation of hydraulic fracturing based on the Navier–Stokes equations coupled with peridynamic theory of solid mechanics through a multi-direct Immersed Boundary Method. The main advantage of this approach consists in the reliable crack-detection and tracking capabilities of peridynamics together with the capability of the Immersed Boundary Method of managing no-slip and no-penetration boundary conditions on complex and time-evolving interfaces. A massive-parallel solver based on this model has been implemented. We present a detailed theoretical description of the proposed methodology as well as the results of an extensive validation campaign for the new solver. Different benchmarking tests are provided together with the qualitative results of a simulation reproducing the fracture of a solid structure in a laminar, unsteady flow.