**4. Problem description**

Stability analysis of the second order spatial centered scheme with the time discretization schemes is performed by two-dimensional simulations of incompressible flows around a stationary circular cylinder. The rectangular domain is chosen to be 15 x *d* 30 with the *d* cylinder located at 16 cylinder diameters from the inlet as .5 illustrated in Fig. (1). The time step used in all simulations is 0.0001 s.

Fig. 1. Schematic illustration of the calculation domain.

The flow develops from the bottom to top and the boundary conditions for velocity are : in the inlet: *u eV* 0 , in the outlet: 0 *<sup>u</sup> y y* and in the lateral boundaries: <sup>0</sup> *<sup>u</sup> x x* . For the pressure, the boundary conditions used are: in the inlet: 0 *<sup>p</sup> y* , in the outlet and in the lateral boundaries: *p* 0 .
