Efficiency and accuracy of stability-guaranteed second-order difference scheme in full-multigrid method

Based on a new stability-guaranteed second-order difference (SGSD) scheme, the full multigrid cycle was implemented in SIMPLE algorithm in order to accelerate convergence of outer-iteration. The difference scheme was implemented by using normalized variable method. The convergence characteristics of full multigrid cycle in SIMPLE algorithm were analyzed by numerical simulation of 2D lid-driven cavity flow. The results show that the SGSD scheme can reach second-order accuracy compared with other high-order schemes and the convergence rate is higher than that of other schemes. The convergence rate of SGSD is 1.77 times that of second-order upwind difference scheme and 1.37 times that of QUICK scheme with Re = 3000, and the stability can be guaranteed in coarse or fine grid. When the multigrid technique is adopted to accelerate the convergence rate, both the circulation pattern and the discretization scheme of convection term should be taken into account. In this regard, the SGSD scheme has an obvious advantage for multigrid implementation.