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.