The analysis of fluid flow near the wellbore region of a hydrocarbon reservoir is a complex phenomenon. The pressure drop and flow rates change in the near wellbore with time, and the understanding of this system is important. Besides existing theoretical and experimental approaches, computational fluid dynamics studies can help understanding the nature of fluid flow from a reservoir into the wellbore. In this research, a near wellbore model using three-dimensional Navier–Stokes equations is presented for analyzing the flow around the wellbore. Pressure and velocity are coupled into a single system which is solved by an algebraic multigrid method for the optimal computational cost. The computational fluid dynamics model is verified against the analytical solution of the Darcy model for reservoir flow, as well as against the analytical solution of pressure diffusivity equation. The streamlines indicate that the flow is radially symmetric with respect to the vertical plane as expected. The present computational fluid dynamics investigation observes that the motion of reservoir fluid becomes nonlinear at the region of near wellbore. Moreover, this nonlinear behavior has an influence on the hydrocarbon recovery. The flow performance through wellbore is analyzed using the inflow performance relations curve for the steady-state and time-dependent solution. Finally, the investigation suggests that the Navier–Stokes equations along with a near-optimal solver provide an efficient computational fluid dynamics framework for analyzing fluid flow in a wellbore and its surrounding region.