A compact-difference scheme for the Navier-Stokes equations in vorticity-velocity formulation

This paper presents a new numerical method for solving the incompressible, unsteady Navier-Stokes equations in vorticity-velocity formulation. The met hod is applicable to spatial simulations of transitional and turbulent boun dary layer flows, It is based on a compact-difference discretization of the streamwise and wall-normal derivatives in Cartesian coordinates. A Fourier collocation approach is used for the spanwise derivatives. Important new f eatures of the numerical method are the use of nonequidistant differences i n the wall-normal direction; the use of split-compact differences in the st reamwise direction; a new, fast iteration for a semi-implicit time integrat ion of the wall-normal diffusion terms; and an improvement of the buffer do main technique to prevent reflections of waves at the outflow boundary. Res ults of test calculations are presented to verify the improvements obtained by the use of these new techniques. (C) 2000 Academic Press.