Advanced Numerical Methods in the Mathematical Sciences
- Sanghyun Lee, University of Texas at Austin
- 3D Fracture Propagation Modeling Using Phase Field
- S. Lee
- A. Mikelic
- M.F. Wheeler
This work presents recent progress in phase-field-based fracture modeling in heterogeneous porous media. We develop robust numerical algorithms that can be used for three-dimensional applications. Specially, we present a Newton loop that combines a primal-dual active set method (required for treating the crack irreversibility)for pressurized fractures and couple this loop with a pressure-diffraction equation in order to solve for fluid flow in the porous media and the fracture.
The resulting algorithm splits geomechanics and flow computations in terms of a fixed-stress approach. Several numerical examples considering pressurized fractures in heterogeneous media and fluid-filled fracture propagation in porous media substantiate our developments.
This is a joint work with A. Mikelic, M.F. Wheeler, and T. Wick.