The objective of the present simulations is to evaluate the applicability of the standard $k-{varepsilon}$ turbulence model in engineering practice in the subcritical to supercritical flow regimes. Two-dimensional numerical simulations of flow around a circular cylinder at $Re=1{ imes}10^5$, $5{ imes}10^5$ and $1{ imes}10^6$, had been performed using Unsteady Reynolds-Averaged Navier Stokes (URANS) equations with the standard $k-{varepsilon}$ turbulence model. Solution verification had been studied by evaluating grid and time step size convergence. For each Reynolds number, several meshes with different grid and time step size resolutions were chosen to calculate the hydrodynamic quantities such as the time-averaged drag coefficient, root-mean square value of lift coefficient, Strouhal number, the coefficient of pressure on the downstream point of the cylinder, the separation angle. By comparing the values of these quantities of adjacent grid or time step size resolutions, convergence study has been performed. Solution validation is obtained by comparing the converged results with published numerical and experimental data. The deviations of the values of present simulated quantities from those corresponding experimental data become smaller as Reynolds numbers increases from $1{ imes}10^5$ to $1{ imes}10^6$. This may show that the standard $k-{varepsilon}$ model with enhanced wall treatment appears to be applicable for higher Reynolds number turbulence flow.