Optimal vorticity conditions for the node-centred finite-difference discretization of the second-order vorticity-velocity equations
The vorticity-velocity formulation of the incompressible Navier-Stokes equations is considered. It is shown that in the framework of the second-order node-centered approximations, the numerical solutions are inferior to those obtained using staggered grids velocity-vorticity and vorticity-stream function equations. To remove this drawback, the wall vorticity condition derived from the approximation of the Stokes theorem applied to each boundary cell is proposed. It is shown that second-order centered discretizations of the all types of equations can be made formally equivalent by imposing this ''optimal'' vorticity condition. Numerical experiments with the driven cavity flow validating the theoretical analysis are described.
scientific article; zbMATH DE number 938019