Abstract: To develop a robust and efficient computational flow simulation tool for
incompressible flow applications, a number of different implicit multigrid
schemes for solving the three-dimensional incompressible Navier-Stokes
equations are compared in the current study. These schemes consist of a
common full approximation storage (FAS) multigrid algorithm implemented
in conjunction with three different implicit schemes, which include a modified
point Gauss relaxation, a standard Gauss-Seidel line relaxation, and the
Beam-Warming alternating direction implicit (ADI) scheme. The flow solver
used in the study is based on artificial compressibility and uses a
third-order upwind difference for the convective terms and a second-order
central difference for the viscous terms. The efficiency of each implicit
multigrid scheme is assessed in terms of the computing time required for
two laminar flow problems: the entry flow through a 90 deg bent square duct,
and the steady-state and unsteady flows past a prolate spheroid at incidence
with an axis ratio of 4 : 1. It is found that implementation of Neumann
boundary conditions on the coarse grid in terms of the flow variable
correction rather than the flow variable itself is essential for
obtaining good convergence in the collocated finite difference discretization.
The results of steady-state flow computations show that all the implicit
multigrid schemes yield more than 50% computational time savings over their
single grid counterparts, and the point or line relaxation multigrid scheme
outperforms the ADI multigrid scheme by at least a factor of 2.
However, in unsteady flow computations, the computational time saving
of the multigrid scheme is less than that in steady-state cases.
The current study concludes that the FAS multigrid algorithm implemented
with the modified point Gauss relaxation scheme is preferable for
simulating both steady-state and time-dependent incompressible flows.