High-resolution simulations of the flow around an impulsively started cylinder using vortex methods

Abstract

The development of a two-dimensional viscous incompressible flow generated from a circular cylinder impulsively started into rectilinear motion is studied computationally. An adaptative numerical scheme, based on vortex methods, is used to integrate the vorticity/velocity formulation of the Navier-Stokes equations for a wide range of Reynolds numbers (Re = 40 to 9500). A novel technique is implemented to resolve diffusion effects and enforce the no-slip boundary condition. The Biot-Savart law is employed to compute the velocities, thus eliminating the need for imposing the far-field boundary conditions. An efficient fast summation algorithm was implemented that allows a large number of computational elements, thus producing unprecedented highresolution simulations. Results are compared to those from other theoretical, experimental and computational works and the relation between the unsteady vorticity field and the forces experienced by the body is discussed.

A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries

“…Figure 20 shows four stages in the evolution of the vortex behind the cylinder at the two Reynolds numbers. These figures compare well with corresponding figures in the paper of Koumoutsakos & Leonard [17]. In Fig.…”

“…Once the BI and the corresponding IP have been identified, a tri-linear interpolant of the following form is used to express the value of a generic variable (say ϕ) in the region between the eight nodes surrounding the image-point: (14) The eight unknown coefficients can be determined in terms of the variable values of the eight surrounding nodes (15) where (16) is the vector containing the eight unknown coefficients and (17) are the values of the variables at the eight surrounding points. Furthermore, [V ] is the Vandermonde matrix [38] corresponding to the trilinear interpolation scheme shown in Eq.…”

“…Flow is simulated at two different Reynolds numbers (Re d = U o d/v) of 550 and 1000, both of which have been simulated using a vortex particle method by Koumoutsakos & Leonard [17]. The current simulations employ dense 541 × 161 grids in order to resolve the extremely thin boundary layers that develop on the cylinder surface.…”

“…In Fig. 21 we have plotted the temporal variation of the computed drag coefficient along with available results from [17] for both cases. It is noted that the current immersed boundary calculations match the results of these previous calculations very well, thereby providing further confidence in the ability of the solver to simulate accurately the production and subsequent convection of vorticity from moving and rapidly accelerating bodies bodies as well as the transient fluid-dynamic forces.…”

Vortex Methods with Spatially Varying Cores

“…In vortex methods Hou [10] first introduced a variable size vortex method for the Euler equations and he demonstrated its convergence. However, the straightforward implementation of Hou's method in the context of viscous vortex methods [11] is not possible due to the moment properties required by the scheme of particle strength exchange for the simulation of diffusion. Instead, as shown in this paper, variable vortex blobs can be incorporated by introducing a mapping between the spatially varying physical domain and a uniform mapped domain.…”