A HIGH-ACCURACY DEFECT-CORRECTION MULTIGRID METHOD FOR THE STEADY INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

The solution of large sets of equations is required when discrete meth ods are used to solve fluid flow and heat transfer problems. Although the cost of the solution is often a drawback when the number of equati ons in the set becomes large, higher order numerical methods can be em ployed in the discretization of differential equations to decrease the number of equations without losing accuracy. For example, using a fou rth-order difference scheme instead of a second-order one would reduce the number of equations by approximately half while preserving the sa me accuracy. In a recent paper, Gupta has developed a fourth-order com pact method for the numerical solution of Navier-Stokes equations. In this paper we propose a defect-correction form of the high order appro ximations using multigrid techniques. We also derive a fourth-order ap proximation to the boundary conditions to be consistent with the fourt h-order discretization of the underlying differential equations. The c onvergence analysis will be discussed for the parameterized form of a general second-order correction difference scheme which includes a fou rth-order scheme as a special case. (C) 1994 Academic Press, Inc.