D. Drikakis et al., Acceleration of multigrid flow computations through dynamic adaptation of the smoothing procedure, J COMPUT PH, 165(2), 2000, pp. 566-591
The paper presents the development and investigation of an adaptive-smoothi
ng (4S) procedure in conjunction with the full multigrid-full approximation
storage method. The latter has been previously implemented by the authors
[1] for the incompressible Navier-Stokes equations in conjunction with the
artificial-compressibility method and forms the basis for investigating the
current AS approach. The principle of adaptive smoothing is to exploit the
nonuniform convergence behavior of the numerical solution during the itera
tions to reduce the size of the computational domain and, subsequently, to
reduce the total computing time. The implementation of the AS approach is i
nvestigated in conjunction with three different adaptivity criteria for two
- and three-dimensional incompressible flows. Furthermore, a dynamic proced
ure (henceforth labeled dynamic adaptivity) for defining variably the AS pa
rameters Juring the computation is also proposed and its performance is inv
estigated in contrast to AS with constant parameters (henceforth labeled st
atic adaptivity). Both static and dynamic adaptivity can provide similar ac
celeration, but the latter additionally provides more stable numerical solu
tions and also requires less experimentation for optimizing the performance
of the method. Numerical experiments are presented for attached and separa
ted hows around airfoils as well as for three-dimensional flow in a curved
channel. For external flows the AS performs better when it is applied in al
l grid levels of the multigrid method, while for internal flows the best pe
rformance is achieved when AS is applied in the finest grid only. Overall,
the results show that substantial acceleration of multigrid computations ca
n be achieved by using adaptive smoothing. (C) 2000 Academic Press.