A Line Search Algorithm for Multiphysics Problems with Fracture Deformation

TL;DR

This paper introduces a tailored line search algorithm for solving highly nonlinear multiphysics problems with fractures, improving convergence by handling discontinuities effectively.

Contribution

A novel, cost-effective line search method that adapts to fracture discontinuities, enhancing solution robustness in complex multiphysics simulations.

Findings

Algorithm successfully solves challenging fracture problems

Proper variable scaling improves convergence

Effective handling of contact state transitions

Abstract

Models for multiphysics problems often contain strong nonlinearities. Including fracture contact mechanics introduces discontinuities at the transition between open and closed or sliding and sticking fractures. The resulting system of equations is highly challenging to solve. The na\"ive choice of Newton's method frequently fails to converge, calling for more refined solution techniques such as line search methods. When dealing with strong nonlinearities and discontinuities, a global line search based on the magnitude of the residual of all equations is at best costly to evaluate and at worst fails to converge. We therefore suggest a cheap and reliable approach tailored to the discontinuities. Utilising adaptive variable scaling, the algorithm uses a line search to identify the transition between contact states. Then, a solution update weight is chosen to ensure that no fracture cells move too far beyond the transition. We demonstrate the algorithm on a series of test cases for poromechanics and thermoporomechanics in fractured porous media. We consider both single- and multifracture cases and study the importance of proper scaling of variables and equations.