on a Staggered Grid

An available code for solving the incompressible Navier-Stokes equations in a channel is studied and modied. The non-uniform grid in normal direction is transformed to a uniform grid by an analytical transformation. The continuous space is discretized with Finite Dierence method on a staggered grid. The code employs the implicit Crank-Nicholson scheme for the linear term and explicit third order Runge-Kutta or Adams-Bashfort for the non-linear term. The modied fractional step method is used for applying the continuity equation into the velocity eld in which the pressure gradient at the previous time step is used in the rst step of the fractional step method. The resulting Poisson equation is solved by applying the Fourier series in two periodic directions while the velocity equations use nite dierences in all directions. The ow in the code is dened for Reynolds numbers based on half channel width and laminar Poiseuille centerline velocity and the initial laminar mass ow rate is kept constant during the iterations by setting the mean pressure gradient at each time step equal to the integrated wall shear stress. The code is modied to be run for Reynold