A numerical‐variational procedure for laminar flow in curved square ducts

A new numerical method is presented for the solution of the Navier–Stokes and continuity equations governing the internal incompressible flows. The method denoted as the CVP method consists in the numerical solution of these equations in conjunction with three additional variational equations for the continuity, the vorticity and the pressure field, using a non‐staggered grid. The method is used for the study of the characteristics of the laminar fully developed flows in curved square ducts. Numerical results are presented for the effects of the flow parameters like the curvature, the Dean number and the stream pressure gradient on the velocity distributions, the friction factor and the appearance of a pair of vortices in addition to those of the familiar secondary flow. The accuracy of the method is discussed and the results are compared with those obtained by us, using a variation of the velocity–pressure linked equation methods denoted as the PLEM method and the results obtained by other methods.