Flux Difference Splitting for Three-Dimensional Steady Incompressible Navier-Stokes Equations in Curvilinear Co-Ordinates

A collocated discretization of the 3D steady incompressible Navier–Stokes equations based on a flux-difference-splitting formulation is presented. The discretization employs primitive variables of Cartesian velocity components and pressure. The splitting used here is a polynomial splitting introduced by Dick and Linden of Roe type. Second-order accuracy is obtained with the defect correction approach in which the state vector is inter-polated with van Leer's κ-scheme. The underlying solution technique to solve the discretized equations is a parallel multiblock multigrid method. Several 2D and 3D test problems such as driven cavity and channel flows are solved.