Analysis of iterative methods for the viscous/inviscid coupled problem viaa spectral element approximation

Based on a new global variational formulation, a spectral element approxima tion of the incompressible Navier-Stokes/Euler coupled problem gives rise t o a global discrete saddle problem. The classical Uzawa algorithm decouples the original saddle problem into two positive definite symmetric systems. Iterative solutions of such systems are feasible and attractive for large p roblems. It is shown that, provided an appropriate pre-conditioner is chose n for the pressure system, the nested conjugate gradient methods can be app lied to obtain rapid convergence rates. Detailed numerical examples are giv en to prove the quality of the pre-conditioner. Thanks to the rapid iterati ve convergence, the global Uzawa algorithm takes advantage of this as compa red with the classical iteration by sub-domain procedures. Furthermore, a g eneralization of the pre-conditioned iterative algorithm to flow simulation is carried out. Comparisons of computational complexity between the Navier -Stokes/Euler coupled solution and the full Navier-Stokes solution are made . It is shown that the gain obtained by using the Navier-Stokes/Euler coupl ed solution is generally considerable. Copyright (C) 2000 John Wiley & Sons , Ltd.