Development of generalized block correction procedures for the solution of discretized navier-stokes equations

Abstract

Numerical prediction of fluid flow involves discretization of the governing partial differential equations followed by solution of the resulting nonlinear coupled equations. Both iterative and direct methods are used for solving these equations. Iterative methods require low storage but are prone to slow convergence. Direct methods on the other hand have robust convergence properties but require large storage. A hybrid method based on a multigrid strategy with two grid levels, which exploits the desirable characteristics of iterative as well as direct methods, is proposed. This solution method uses iterative techniques for solution on the fine grid and solves directly for correction quantities on the coarse block-correction grid. Results show that the proposed method yields a significant reduction in the computational effort in comparison to conventional iterative as well as direct methods. The block correction procedure embedded in the proposed method can also be used very effectively for accelerating the convergence fo subdomain methods.