On spurious vortical structures

The paper investigates the formation of spurious vortical structures in inc ompressible flow simulations employing Godunov-type methods. The present wo rk 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 partic ular) that spurious vortices can occur in underresolved flow simulations. T he aim of our work is threefold: (i) to identify deficiencies in various Go dunov-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 solu tions even under insufficient grid resolution. Our results reveal that the occurrence of spurious solutions depends strongly on the Godunov-type metho d employed. We show that in addition to the dissipation properties of a sch eme-emphasized by Brown and Minion-there are other factors that can also co ntribute to numerical artifacts. These include a vortical instability arisi ng from the numerical discretization of the advective terms in the primitiv e variable formulation of the Navier-Stokes equations, the balance of dissi pation among the different discretized terms in a Godunov-type method. as w ell as order of accuracy of the interpolation used to discretize the wave-s peed dependent term of the Godunov flux. (C) 2001 Academic Press.