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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
  • T.Wick


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.