Computational Analysis of Incompressible Pipe Flow in Sudan: Numerical Method Comparison and Navier-Stokes Validation

This study presents a detailed numerical investigation of axisymmetric, incompressible, pressure-driven flow in circular pipes representative of two major pipeline systems in Sudan: The Greater Nile (GN) and Petrodar (PD) pipelines. Both simplified numerical simulation approaches and a full Navier-Stokes solver are employed to analyze axial velocity profiles, pressure distributions, and vorticity fields. Velocity and pressure are computed using finite-difference, finite-volume, and finite-element methods, with successive over-relaxation (SOR) applied to assess residual convergence and numerical stability. The complete Navier-Stokes solver explicitly accounts for radial momentum diffusion, enabling accurate prediction of steady-state axial velocity and azimuthal vorticity. Numerical results are validated through comparison with the analytical Poiseuille flow solution. The findings highlight the effects of fluid viscosity and imposed pressure gradients on velocity and vorticity distributions, revealing noticeable differences between the GN and PD pipelines. Overall, the study provides valuable insight into numerical modelling and validation of laminar-to-transitional pipe flow for practical engineering applications.