A computational comparison of two incompressible Navier-Stokes solvers in three-dimensional laminar flows

A finite-analytic and a finite-difference based numerical method for solving the incompressible Navier-Stokes equations are described and their spatial resolution and overall performance are scrutinized through careful analysis of the discrete equations and numerical experimentation. To facilitate a fair and unbiased comparison, both methods are applied on identical numerical grids to calculate three-dimensional laminar flows through strongly curved square ducts. Detailed comparisons between the computed solutions and the experimental data reveal significant discrepancies between the two numerical predictions. These discrepancies, which are attributed to the different strategies each numerical method adopts for discretizing the governing flow equations, clearly underscore the importance of developing reliable numerical methods which can accurately describe the physics of complex, three-dimensional flow fields.