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Textbook Multigrid Efficiency for Computational Fluid DynamicsColloquium
|Speaker: ||Dr. Boris Diskin, ICASE, NASA Langley Research Center|
|Location: ||693 Kerr|
|Start time: ||Wed, Apr 25 2001, 4:10PM|
Full multigrid (FMG) algorithms are the fastest solvers
for elliptic problems. These algorithms can solve a general
discretized elliptic problem to the discretization accuracy
in a computational work that is a small (less than 10) multiple
of the operation count in one target-grid residual
evaluation. Such efficiency is known as textbook multigrid efficiency
(TME). The difficulties associated with extending
TME for solution of the Reynolds-averaged
Navier-Stokes (RANS) equations relate to the fact that the
RANS equations are a system of coupled nonlinear equations
that is not, even for subsonic Mach numbers, fully elliptic, but
contain hyperbolic partitions. TME for the RANS simulations
can be achieved if the different factors contributing to
the system could be separated and treated
optimally, e.g., by multigrid for elliptic factors
and by downstream marching for hyperbolic factors.
One of the ways to separate the factors is the distributed
relaxation approach. Earlier demonstrations of TME solvers with
distributed relaxation have already been performed for
relatively simple subsets of RANS equations in simple
geometries (incompressible free-stream inviscid and viscous
flows without boundary layers).
In this talk, I am going to briefly outline
the basic multigrid ideas
and their applications to solution of PDE.
The concept of distributed
relaxation will be discussed in more details.
A general framework for achieving TME
in solution of the Navier-Stokes
equations will be presented. Some numerical results
confirming TME for distributed-relaxation solvers
will be demonstrated for
viscous incompressible and subsonic compressible flows
with boundary layers and for inviscid compressible transonic
flows with shocks.
Refreshment is served in 693 Kerr at 3:45pm.