Numerical simulation of three dimensional flows in duct

The validity of various simplifying assumptions for reducing the number of variables in the Navier-Stokes equations for numerical computations of incompressible viscous flows is examined. Attention is focused on flows in a channel with a square cross-section. Two simplification methods are investigated for parabolization of the equations, and one multigrid technique is explored. The schemes are applied to flows at the entrance of a rectangular duct with Re between 10 and 1000. Error parameters are defined for comparing the accuracy of the two methods involving a parabolization of the equations. It is found that errors due to simplifying assumptions can be avoided by using a multigrid technique, which will be accompanied by only a small increase in computing time.