On analogy and dissimilarity of dependence of stability on several parameters in flow simulations

In the present paper, we investigate the asymptotic behavior of numerical solutions in direct fluid simulations. The incompressible Navier–Stokes equations and the continuity equation are solved numerically by using the marker-and-cell method. The model adopted in the present study is a flow around a two-dimensional circular cylinder. Dependence of the unsteady structure of numerical solutions on several parameters are discussed by analyzing the behavior of numerical drag coefficient Cd. Concretely, we concentrate the dependence of bifurcation processes on the amplitude of second- and fourth-order viscosity terms and time increment. Though the numerical fourth-order artificial viscosity has the stabilizing effect like the physical second-order one, the bifurcation processes are different. Furthermore, it is clarified that adopting small time increment values does not always produce the reasonable results.