Block-implicit multigrid solution of Navier-Stokes equations in primitive variables

Abstract A calculation procedure for rapid computation of steady multidimensional viscous flows is presented. The method solves the Navier-Stokes equations in primitive variables using a coupled block-implicit multigrid procedure. The procedure is applicable to finite-difference formulations using staggered locations of the flow variables. A smoothing technique called symmetrical coupled Gauss-Seidel (SCGS) is proposed and is empirically observed to provide good smoothing rates. The viscous flow in a square cavity with a moving top wall is calculated for a range of Reynolds numbers. Calculations with finite difference grids as large as 321 × 321 nodes have been made to test the accuracy and efficiency of the calculation scheme. The CPU times for these calculations are observed to be significantly smaller than other solution algorithms with primitive variable formulation. The calculated flow fields in the cavity are in good agreement with earlier studies of the same flow situation.