A semi-Lagrangian finite volume method for Newtonian contraction flows

A new finite volume method for solving the incompressible Navier Stokes equ ations is presented. The main features of this method are the location of t he velocity components and pressure on different staggered grids and a semi -Lagrangian method for the treatment of convection. An interpolation proced ure based on area-weighting is used for the convection part of the computat ion. The method is applied to ow through a constricted channel, and results are obtained for Reynolds umbers, based on half the ow rate, up to 1000. T he behavior of the vortex in the salient corner is investigated qualitative ly and quantitatively, and excellent agreement is found with the numerical results of Dennis and Smith [Proc. Roy. Soc. London A, 372 ( 1980), pp. 393 -414] and the asymptotic theory of Smith.