OPTIMIZED DUAL-TIME STEPPING TECHNIQUE FOR TIME-ACCURATE NAVIER-STOKES CALCULATIONS

This paper presents an optimized discretization of the time derivative term for the dual-time stepping method. The proposed discretization is second order accurate and has a lower level of dissipation and dispersion errors than the conventional non-optimized second order discretization. Sample calculations demonstrate that the optimized scheme requires approximately 45-50% less time steps per unsteady cycle compared to the standard non-optimized scheme to resolve an unsteady flow within a certain margin of amplitude error. The number of time steps per cycle can be reduced by 10-15% to keep the phase error less than a certain level when the optimized scheme is used. Since time-accurate calculations are expensive, the proposed approach leads to significant savings of computational time and resources.