Preconditioning for the Steady-State Navier-Stokes Equations with Low
Viscosity
Preconditioning for the Steady-State Navier-Stokes Equations with Low
Viscosity
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Date
1998-10-15
Authors
Elman, Howard C.
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Abstract
We introduce a preconditioner for the linearized Navier-Stokes equations
that is effective when either the discretization mesh size or the viscosity
approaches zero.
For constant coefficient problems with periodic boundary conditions, we
show that the preconditioning yields a system with a single eigenvalue
equal to one, so that performance is independent of both viscosity and
mesh size. For other boundary conditions, we demonstrate empirically that
convergence depends only mildly on these parameters and we give a partial
analysis of this phenomenon.
We also show that some expensive subsidiary computations required by the new
method can be replaced by inexpensive approximate versions of these tasks
based on iteration, with virtually no degradation of performance.
(Also cross-referenced as UMIACS-TR-96-82)