Work

A time step-size computing arc-length method for the phase-field hydraulic fracture model

Year: 2024

Type: article

Abstract: The phase-field hydraulic fracture model entails a non-convex energy functional. This renders a poor convergence behaviour for monolithic solution techniques, such as the Newton-Raphson method. Consequently, researcher have adopted alternative solution techniques such as the staggered solution technique and the Newton-Raphson method with convexification via extrapolation of the phase-field. Both methods are robust. However, the former is computationally expensive and in the latter, the extrapolation itself is questionable w.r.t regularity in time. In this work, a novel dissipation-based arc-length method is proposed as a robust and computationally efficient monolithic solution technique for the phase-field hydraulic fracture model. Since hydraulic fracturing problems are quite often driven by constant flux, scaling of the external force is not possible. Instead, the time step-size is considered as the additional unknown, augmenting the arc-length constraint equation. The robustness and computational efficiency of the proposed arc-length method is demonstrated using numerical experiments, where comparisons are made with the staggered solver as well as the quasi-Newton BFGS method.

Source: Computer Methods in Applied Mechanics and Engineering

DOI: 10.1016/j.cma.2024.117687

Authors: Ritukesh Bharali, Frans P. van der Meer, Fredrik Larsson, Ralf Jänicke

Institutions: Chalmers University of Technology, Technische Universität Braunschweig

Language: English

Topic: Hydraulic Fracturing and Reservoir Analysis

Subfield: Mechanical Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,660

Funders: Technische Universiteit Delft, Svenska Forskningsrådet Formas, Vetenskapsrådet