Acceleration of multigrid flow computations through dynamic adaptation of the smoothing procedure

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.