Box-Line Relaxation Schemes for Solving the Steady Incompressible Navier-Stokes Equations Using Second-Order Upwind Differencing

Abstract

We extend the SCGS smoothing procedure (Symmetrical Collective Gauss-Seidel relaxation) proposed by S. P. Vanka$^{[4]}$, for multigrid solvers of the steady viscous incompressible Navier-Stokes equations, to corresponding line-wise versions. The resulting relaxation schemes are integrated into the multigrid solver based on second-order upwind differencing presented in [5]. Numerical comparisons on the efficiency of point-wise and line-wise relaxations are presented.