Globalization strategies for inexact-Newton solvers

Globalization strategies are necessary in practical inexact-Newton flow solvers to ensure convergence when the initial iterate is far from the solution. In this work, we present two novel globalizations based on parameter continuation. The first continuation method parameterizes the boundary conditions while the second parameterizes the numerical dissipation. In both cases, a continuation parameter is used to create a sequence of modified nonlinear equations. The solution of each equation in the sequence provides an initial estimate for the subsequent problem until the desired convergence tolerance is reached. When applied to benign inviscid flows, the proposed globalization methods have similar efficiency compared with the more common pseudo-transient continuation. They are significantly more robust on difficult inviscid problems. Moreover, the continuation-based methods require less tuning.