Numerical Analysis of Navier–Stokes Equations for Multi-Layer Incompressible Flows Utilizing Finite Difference Method and Finite Volume Method

This research focuses on the numerical simulation of stratified incompressible multi-fluid flows, particularly in multi-fluid oil transport systems. The traditional models built on homogeneous fluids do not capture well the complexities brought about by changes in density and viscosity across immiscible layers. To overcome this challenge, the Finite Difference Method (FDM) and Finite Volume Method (FVM) are applied to solve the Navier–Stokes equations in a layered manner. The computational domain is a two-dimensional pipeline geometry with an oil-water interface, undergoing isothermal and incompressible flow. The dynamics of the interface are described by stepwise density functions with continuity conditions for velocity and shear stress. The simulations are done in Octave, and results confirm the advantages of FVM in conservation properties, interface handling, and complex geometry applications. The results show that robust discretization techniques are critical for accurately predicting flow behavior in industrial multi-fluid transport systems.