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# Fast Scheme to Analyze Three Dimensional Airflow for Computer Disks on Massively Parallel Computer

IP.com Disclosure Number: IPCOM000115771D
Original Publication Date: 1995-Jun-01
Included in the Prior Art Database: 2005-Mar-30
Document File: 4 page(s) / 133K

IBM

## Related People

Chang, CJ: AUTHOR [+2]

## Abstract

The disclosed method concerns the parallel algorithms in the numerical calculation of the airflow for the following configuration: several disks are concentrically and equidistantly fixed along a rotary hub, and placed in a stationary circular enclosure; an arm is located in the symmetry plane between each pair of disks. The hub and the disks rotate at a fixed speed while the arm stays stationary at a certain penetration depth.

This text was extracted from an ASCII text file.
This is the abbreviated version, containing approximately 45% of the total text.

Fast Scheme to Analyze Three Dimensional Airflow for Computer Disks
on Massively Parallel Computer

The disclosed method concerns the parallel algorithms in the
numerical calculation of the airflow for the following configuration:
several disks are concentrically and equidistantly fixed along a
rotary hub, and placed in a stationary circular enclosure; an arm is
located in the symmetry plane between each pair of disks.  The hub
and the disks rotate at a fixed speed while the arm stays stationary
at a certain penetration depth.

Many methods are possible in parallelizing the computation of
the disk airflow formulated from the finite difference form of
Navior-Stokes equations.  For a given finite difference decomposition
of the disk, each node in the grid is connected to six neighboring
nodes.  Equivalently, the very node and the neighboring nodes are
represented by the 7-variable equation.  When these variables are
treated as implicit, a 7-band matrix of size NxN is formed where
N=ZRT is the total number of nodes in the grid, and Z, R and T are
the numbers of the grid decomposition in the axial, radial and
tangential direction, respectively.  Such a matrix can be solved
sequentially or in parallel as studied in many parallel numerical
algorithms.  Noticed, however, that other methods of parallelizing
the solving of the disk airflow are possible if the characteristics
of the flow can be considered.

One such consideration is the mechanism of the momentum
transfer from the solid boundary to the fluid during the iteration.
Observe that in the tangential direction, the velocity gradient is
small due to the strong convection effect by the dominant tangential
velocity.  Consequently, one can treat the variables at the upstream
and downstream nodes as explicit and expect that such a solving will
not affect the quality of the solution while increasing the degree of
the parallelism.  The single 7-band matrix is therefore reduced to T
5-band matrices, each of which is of size ZRxZR.  These T matrices
can be solved in parallel due to the decoupling of the variables in
the tangential direction from others.

By the same token, more variables can be treated as explicit
and more parallelism can be obtained.  One such approach is to
further treat the variables at the east and west nodes as explicit,
which leads to RT tri-diagonal matrices each of size ZxZ.  It is
expected that such a decoupling will not affect the solution quality
based on the observation that a boundary layer is formed on the
surface of the disk and the momentum transfer in the z-direction is
higher than that in the r-direction.  In this method, many "grid
lines" along z-direction can be used to solve the flow field in
parallel.  This method is called Line Parallel Algorithm For maximum
parallelism, decouple all variables and make them all explicit.  This
leads to ZRT 1x1 matrices or points.  This approach is called Point
Parallel Algori...