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.

翻译：多物理场问题的模型通常包含强非线性特性。引入裂缝接触力学会在裂缝张开与闭合或滑动与黏着状态之间的过渡区域产生不连续性，由此得到的方程组求解极具挑战性。直接采用牛顿法常难以收敛，因此需要更精细的求解技术，例如线搜索方法。在处理强非线性和不连续问题时，基于所有方程残差范数的全局线搜索方法评估成本极高，甚至可能无法收敛。为此，我们提出一种针对不连续性问题设计的低成本可靠方法。该算法利用自适应变量缩放，通过线搜索识别接触状态间的过渡区域，进而选择解更新权重以确保裂缝单元不会过度跨越过渡边界。我们在裂隙多孔介质中的孔隙力学与热孔隙力学系列测试案例中验证了该算法，涵盖了单裂缝与多裂缝情形，并研究了变量与方程适当缩放的重要性。