214	1999	Henrik Brandén	henrik@tdb.uu.se	Convergence Acceleration for Flow Problems using Semicirculant Approximations

			Abstract

We study a semicirculant preconditioning technique for the iterative 
solution of time-independent compressible flow problems, governed by the 
linearized Euler or Navier--Stokes equations. The PDEs are discretized on
structured grids using finite difference or finite volume methods, and
the solution is computed by integrating the corresponding time-dependent,
preconditioned problems in time. 

We derive relevant model problems for which we prove that the preconditioned 
coefficient matrix asymptotically has a bounded spectrum. We study the
time step for the basic forward Euler iteration, and show
that it may be chosen as a constant, independent of the grid size
and, for the case of viscous flow, the Reynolds number.

Numerical experiments verifies that the forward Euler method can be used 
also for the Euler and Navier--Stokes equations, in the same way as for the 
model problems. We compare the results to those for a multigrid method, and 
it is clear that the semicirculant preconditioning technique is more efficient.
Furthermore, the multigrid method is sensitive to the amount of artificial 
viscosity, while the semicirculant preconditioning technique is not.