Electronic, Magnetic and Chemical Properties of Films, Surfaces and Alloys

Fourth-order compact differencing is applied to the steady solution of two-dimensional viscous incompressible flows at moderate Reynolds number. The physical region where the fluid flow occurs is mapped onto a rectangle by means of the boundary-fitted coordinates transformation method. The design of the general numerical algorithm rests upon discretization of velocity components and pressure field at the same grid points. The validity of this procedure is assessed by the investigation of a Stokes test problem. Fourth-order numerical results are compared to the analytical solution, second-order results and Chebyshev tau approximation. It is shown that fourth-order differences provide good precision, particularly when the ability of generating irregular meshes is fully exploited. Standard problems as Poiseuille and Couette flows, and the square cavity problem are solved. The fourth-order results on coarse mesh compare favourably with other techniques such as finite element method and second-order differences. A global convergence analysis was performed. On a two-dimensional problem with smooth boundary conditions, one observes a rate of convergence of order four for the velocity components and of order three for the pressure. For the square cavity problem with the two corner singularities, the rates of convergence are decreased by almost an order of magnitude. The solution of a plane constricted channel flow enhances the overall improvement in accuracy, gained by the treatment of the geometrically complex region through the mapping technique.