On Spurious Vortical Structures

The paper investigates the formation of spurious vortical structures in incompressible flow simulations employing Godunov-type methods. The present work is motivated by the earlier studies of Brown and Minion (1995, J. Comput. Phys.122, 165 and 1997, J. Comput. Phys.138, 734) who demonstrated for a variety of numerical schemes (and for the upwind-biased methods in particular) that spurious vortices can occur in underresolved flow simulations. The aim of our work is threefold: (i) to identify deficiencies in various Godunov-type methods leading to spurious flow structures, (ii) to examine the numerical mechanisms responsible for these artifacts, and (iii) to propose modifications of Godunov-type methods in order to recover the correct solutions even under insufficient grid resolution. Our results reveal that the occurrence of spurious solutions depends strongly on the Godunov-type method employed. We show that in addition to the dissipation properties of a scheme—emphasized by Brown and Minion—there are other factors that can also contribute to numerical artifacts. These include a vortical instability arising from the numerical discretization of the advective terms in the primitive variable formulation of the Navier–Stokes equations, the balance of dissipation among the different discretized terms in a Godunov-type method, as well as order of accuracy of the interpolation used to discretize the wave-speed dependent term of the Godunov flux.