A Phase-Field Description for Pressurized and Non-Isothermal Propagating Fractures
This work provides a robust numerical framework for simulating pressurized, non-isothermal fractures, which is important for geomechanics and reservoir engineering applications.
The authors extended a phase-field approach for pressurized fractures to non-isothermal settings, correctly modeling interface laws between porous medium and fracture. Numerical examples in 2D and 3D verified the implementation, with excellent performance of nonlinear and linear solvers.
In this work, we extend a phase-field approach for pressurized fractures to non-isothermal settings. Specifically, the pressure and the temperature are given quantities and the emphasis is on the correct modeling of the interface laws between a porous medium and the fracture. The resulting model is augmented with thermodynamical arguments and then analyzed from a mechanical perspective. The numerical solution is based on a robust semi-smooth Newton approach in which the linear equation systems are solved with a generalized minimal residual method and algebraic multigrid preconditioning. The proposed modeling and algorithmic developments are substantiated with different examples in two- and three dimensions. We notice that for some of these configurations manufactured solutions can be constructed, allowing for a careful verification of our implementation. Furthermore, crack-oriented predictor-corrector adaptivity and a parallel implementation are used to keep the computational cost reasonable. Snapshots of iteration numbers show an excellent performance of the nonlinear and linear solution algorithms. Lastly, for some tests, a computational analysis of the effects of strain-energy splitting is performed, which has not been undertaken to date for similar phase-field settings involving pressure, fluids or non-isothermal effects.