Improvements to a Dual-Time-Stepping Method for Computing Unsteady Flows

The nonlinear problem to be solved within an implicit time-marching method has several differences from a typical steady-state problem. The initial guess is usually quite good, and the degree of convergence required is quite small, perhaps a few orders of magnitude reduction in residual. Therefore, algorithms developed for steady problems may not be optimal for use in a dual-time context. We present some modifications to the diagonal approximately factored algorithm that lead to savings in a dual-time-stepping context.