High-order accurate methods for unsteady vortical flows on curvilinear meshes

This paper investigates several issues related to the application of very high-order schemes for the finitedifference simulation of the full Navier-Stokes equations. The schemes utilize an implicit, approximately factored time-integration method coupled with spatial fourthand sixth-order compact-difference formulations and a filtering strategy of up to tenth-order. For this last aspect, a consistent optimization strategy is developed to treat points near the boundary resulting in minimal degradation of accuracy. The problems investigated exhibit many of the challenging features of practical flows, and include several with complications introduced by curvilinear meshes, viscous effects, unsteadiness and three-dimensionality. The high-order method is observed to be very robust for every problem considered. The algorithm is demonstrated to be highly accurate (both absolutely and in order of accuracy) compared to both second-order and upwind-biased methods. For several cases, particularly very low-Mach number flows, filtering is determined to be a superior alternative to damping.

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