[Paper Review] A fully-coupled computational framework for large-scale simulation of fluid-driven fracture propagation on parallel computers

Bianca Giovanardi, Santiago Serebrinsky+1 more|arXiv (Cornell University)|Nov 22, 2019

Numerical methods in engineering64 references23 citations

TL;DR

This paper presents a fully-coupled, massively parallel computational framework for simulating fluid-driven fracture propagation in 3D, using a high-order hybrid discontinuous Galerkin/cohesive zone model for solid mechanics and continuous finite elements for lubrication flow within cracks. The method achieves robust convergence via Newton-Raphson iteration and demonstrates scalability up to 30 million degrees of freedom on 700 processors, enabling accurate simulation of complex crack paths including branching and merging without predefined crack trajectories.

ABSTRACT

The propagation of cracks driven by a pressurized fluid emerges in several areas of engineering, including structural, geotechnical, and petroleum engineering. We present a robust numerical framework to simulate fluid-driven fracture propagation that addresses the challenges emerging in the simulation of this complex coupled nonlinear hydro-mechanical response. We observe that the numerical difficulties stem from the strong nonlinearities present in the fluid equations as well as those associated with crack propagation, from the quasi-static nature of the problem, and from the a priori unknown and potentially intricate crack geometries that may arise. An additional challenge is the need for large scale simulation owing to the mesh resolution requirements and the expected 3D character of the problem in practical applications. To address these challenges we model crack propagation with a high-order hybrid discontinuous Galerkin / cohesive zone model framework, which has proven massive scalability properties, and we model the lubrication flow inside the propagating cracks using continuous finite elements, furnishing a fully-coupled discretization of the solid and fluid equations. The parallel approach for solving the linearized coupled problem consists of standard iterative solvers based on domain decomposition. The resulting computational approach provides the ability to conduct highly-resolved and quasi-static simulations of fluid-driven fracture propagation with unspecified crack path. We conduct a series of numerical tests to verify the computational framework against known analytical solutions in the toughness and viscosity dominated regimes and we demonstrate its performance in terms of robustness and parallel scalability, enabling simulations of several million degrees of freedom on hundreds of processors.

Motivation & Objective

• To address the challenges of simulating fluid-driven fracture propagation in 3D with arbitrary, evolving crack paths.
• To overcome numerical instabilities arising from strong hydro-mechanical coupling, nonlinear fluid flow, and crack propagation in quasi-static conditions.
• To enable large-scale simulations with high mesh resolution and parallel scalability for practical engineering applications.
• To develop a robust, fully-coupled discretization that avoids convergence issues inherent in staggered solution strategies.
• To validate the framework against analytical solutions in toughness- and viscosity-dominated regimes and demonstrate performance on complex crack morphologies.

Proposed method

• A hybrid discontinuous Galerkin/cohesive zone model (DG/CZM) is used to model solid deformation and crack propagation with high-order accuracy and massive parallel scalability.
• Continuous finite elements are employed to discretize the lubrication flow equations within evolving crack interfaces, ensuring accurate fluid pressure and opening field calculations.
• The fully-coupled system of solid and fluid equations is solved using a Newton-Raphson algorithm with fixed fluid domain during nonlinear iterations to ensure robust convergence.
• Domain decomposition-based iterative solvers are used for the linearized system, enabling efficient solution on distributed memory parallel architectures.
• Crack propagation is tracked implicitly through the cohesive zone model, allowing arbitrary crack paths without remeshing or path constraints.
• The framework maintains a fixed fluid domain during Newton iterations and updates it only upon convergence, preserving stability and accuracy.

Experimental results

Research questions

• RQ1 Can a fully-coupled, monolithic solution strategy overcome the ill-posedness and convergence issues of staggered schemes in fluid-driven fracture simulations?
• RQ2 How well does the proposed framework reproduce analytical solutions for plane-strain and penny-shaped crack geometries in both toughness- and viscosity-dominated regimes?
• RQ3 To what extent can the method simulate complex crack morphologies such as branching and merging without predefined crack paths?
• RQ4 What level of parallel scalability can be achieved for large-scale 3D fluid-driven fracture simulations using this framework?
• RQ5 How does the choice of fixed fluid domain during Newton iterations impact the robustness and convergence of the nonlinear solver?

Key findings

• The fully-coupled Newton-Raphson approach demonstrated robust convergence even in the presence of complex, evolving crack paths, outperforming staggered schemes that suffer from ill-posedness and convergence failure.
• The framework accurately reproduces analytical solutions for plane-strain and penny-shaped cracks, validating the accuracy of the fluid pressure and crack opening fields.
• The method successfully simulates crack branching and merging, including the activation of pre-existing dry cracks via fluid injection, with realistic pressure and stress evolution.
• Strong scaling analysis shows a reduction in wall time per time step from 53 minutes (4 processors) to 47 seconds (256 processors) for a 1.8 million degree-of-freedom problem.
• The framework achieves massive scalability up to 30 million degrees of freedom on 700 processors, with wall time per time step decreasing from 57 minutes (350 processors) to 22 minutes (700 processors).
• The use of a fixed fluid domain during Newton iterations ensures stability and convergence, while the hybrid DG/CZM formulation enables accurate crack path prediction without remeshing.