An efficient multigrid acceleration for colving the 3-D incompressible navier-stokes equations in generalized curvilinear coordinates

摘要

In this paper, an efficient multigrid algorithm is presented for solving the three-dimensional incompressible Navier-Stokes equations for practical engineering problems. THe artifiial compressibility form of the equations is discretized in a finite volume form on a time-dependent curvilinear coordinate system, and the so-called Discretized Newton-Relaxation (DNR) scheme is used as the iterative procedure for the solution of the system of equations. A nonlinear multigrid scheem (FAS) is applied to accelerate te convergence of the time-dependent equations to a steady state. Two methods for constructing the coarse grid operator, the Galerkin coarse grid approximation (GCA) and the discrete coarse grid approximation (DCA), have also been investigated and incorporated into the FAS scheme. Experiments show that the Galerkin coarse grid approximation provides better performance for the multigrid scheme than the discrete coarse grid approximation.