A choice of forcing terms in inexact Newton iterations with application to pseudo-transient continuation for incompressible fluid flow computations

A strategy for choosing the forcing terms in inexact Newton iterations is presented. The final goal is to obtain fast steady state marching strategies for the solution of PDEs. The new approach is analyzed and tested in the context of inexact Newton methods but is also well suited to be applied in the pseudo-transient continuation framework. To validate the strategy and assess its gains in terms of computational costs we seek approximate solutions of the incompressible Navier-Stokes equations at high-Reynolds numbers. In particular we consider the well known 2D lid-driven cavity flow and backward-facing step problem focusing on the efficiency of the time marching strategy. Residual history and computation time are monitored and compared with many fixed and adaptive forcing term choices of reference.