Cell centered and cell vertex multigrid schemes for the Navier-Stokes equations

Abstract

Two efficient and robust finite-volume multigrid schemes for solving the Navier-Stokes equations are investigated. These schemes employ either a cell centred or a cell vertex discretisation technique. An explicit Runge-Kutta algorithm is used to advance the solution in time. Acceleration techniques are applied to obtain faster steady-state convergence. Accuracy and convergence of the schemes are examined. Computational results for transonic airfoil flows are essentially the same, even for a coarse mesh. Both schemes exhibit very good convergence rates for a broad range of artificial dissipation coefficients.