In this paper, a model has been presented for generating a special ring vortex by applying a nonconservative force with specific distribution through the Navier-Stokes equations. Moreover, the ring's vortical pattern has been compared with the analytical and experimental results. In continuation, the diffusion, dissipation, and dispersion errors of four basic convection term interpolation schemes for the velocity and vorticity field of the vortex ring have been investigated. The simulations are performed for both the small and large time steps. Next, an appropriate discretization scheme for the convection term, and a proper order of time steps for simulating flows that contain ring vortices have been proposed. Finally, the ring vortexes generated by non-conservative force are added to the turbulent channel flow as a bubble induced vortex on carrier flow in two-phase flows, and the drag reduction due to the interaction between ring vortexes and flow vorticity field is observed.