Integration of Navier–Stokes Equations Using Dual Time Stepping and a Multigrid Method

Efficient acceleration techniques typical of explicit steady-state solvers are extended to time-accurate calculations. Stability restrictions are greatly reduced by means of a fully implicit time discretization. A four-stage Runge-Kutta scheme with local time stepping, residual smoothing, and multigridding is used instead of traditional computationally expensive factorizations. Two applications to natural unsteady viscous flows are presented to check for the capability of the procedure.