Multigrid algorithm for three-dimensional incompressible high-Reynolds number turbulent flows

Abstract

A robust multigrid algorithm is presented for solving three-dimensional incompressible high-Reynolds number turbulent flows on high aspect ratio grids. The artificial compressibility form of the Navier-Stokes equations is discretized in a cell-centered finite volume form on a time-dependent curvilinear coordinate system, and the so-called discretized Newton-relaxation scheme is used as the iterative procedure for the solution of the system of equations. A nonlinear multigrid 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 coarse grid approximation and the discrete coarse grid approximation have also 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 number turbulent flows for practical engineering problems are presented to illustrate the efficiency and accuracy of the current multigrid algorithm.