Newton Method for Nonlinear Dynamic Systems with Adaptive Time Stepping

This paper presents a nonlinear solver based on the Newton-Krylov methods, where the Newton equations are solved by Krylov-subspace type approaches. We focus on the solution of unsteady systems, in which the temporal terms are discretized by the backward Euler method using finite difference. To save computational cost, an adaptive time stepping is used to minimize the number of time steps. The developed program can be applied to solve any nonlinear equations, provided the users could supply the discrete form of the equations. In particular, the nonlinear solver is implemented to solve unsteady reacting flows.