Graduate School in Nonlinear Science

Sponsored by the Danish Research Academy

MIDIT                               OFD                           CATS
Modelling, Nonlinear Dynamics       Optics and Fluid Dynamics     Chaos and Turbulence Studies
and Irreversible Thermodynamics     Risø National Laboratory      Niels Bohr Institute and 
Technical University of Denmark     Building 128                  Department of Chemistry
Building 321                        P.O. Box 49                   University of Copenhagen 
DK-2800 Lyngby                      DK-4000 Roskilde              DK-2100 Copenhagen Ø
Denmark                             Denmark                       Denmark


by Chuanju XU
Department of Mathematics
Xiamen University
361005 Xiamen

Laboratoire J.A. Dieudonne de Mathematiques,
UNSA, 06108 Nice, France

Tuesday June 15, 1999, 14-15 h
at ET, Institute of Energy Engineering
Fluid Mechanics, Building 404, Room 215

Abstract: Efficient methods are proposed to solve the non-linear incompressible Navier-Stokes/Euler coupled equations. Based on a new global variational formulation, the coupled problem gives rise to a global saddle problem. Classical Uzawa algorithm decouples the original saddle problem into two positive definite symmetric systems. It is shown that, provided appropriate preconditioner is chosen for the pressure system, the nested conjugate gradient methods can be applied to obtain rapid convergence rate.
An iteration-by-subdomain method has also been investigated. The convergences are proven both in the differential case and in their spectral collocation counterpart. Detailed analysis shows that the iterative algorithms converge with a rate independent of the polynomial degree. A validation study is carried out by simulating the flow past a cylinder.