MULTIGRID ALGORITHM FOR 3-DIMENSIONAL INCOMPRESSIBLE HIGH-REYNOLDS NUMBER TURBULENT FLOWS

In this paper, a robust multigrid algorithm is presented for solving t hree-dimensional incompressible high-Reynolds number turbulent hows on high aspect ratio grids. The artificial compressibility form of the N avier-Stokes equations is discretized in a cell-centered finite volume form on a time-dependent curvilinear coordinate system, and the so-ca lled discretized Newton-relaxation scheme is used as the iterative pro cedure for the solution of the system of equations. A nonlinear multig rid scheme (full approximation scheme [FAS]) is applied to accelerate the convergence of the time-dependent equations to a steady state. Two methods for constructing the coarse grid operator, the Galerkin coars e grid approximation and the discrete coarse grid approximation have a lso been investigated and incorporated into the FAS. A new procedure, called implicit correction smoothing that leads to high efficiency of the multigrid scheme by allowing large Courant-Friedrichs-Lewy numbers , is introduced in this work. Numerical solutions of high-Reynolds num ber turbulent bows for practical engineering problems are presented to illustrate the efficiency and accuracy of the current multigrid algor ithm.