Algorithm Basics for OVERFLOW-D
The methods developed for OVERFLOW-D are
motivated by the need for adaptive refinement capability to maintain solution accuracy for
geometrically complex problems, and by a desire to exploit the many advantages inherent to
structured data available in systems of overset structured grids. The method of adaptive
refinement in OVERFLOW-D is one of adaptive spatial partitioning and refinement. The
physical domain for a given problem is divided into "near-body" and
"off-body" regions. The near-body portion of a domain is defined to include the
surface geometry of all bodies being considered and the volume of space extending a short
distance away from the respective surfaces. The construction of near-body grids and
associated intergrid connectivity is a classical Chimera-style decomposition of the
near-body domain. In the present case, it is assumed that near-body grids provide grid
point distributions of sufficient density to accurately resolve the flow physics of
interest (i.e., boundary-layers, vortices, etc.) without the need for refinement. This is
a reasonable constraint since near- body grids are only required to extend a short
distance away from body surfaces. However, in the future, if the need exists, a method of
adaptive refinement within near- body grids will also be developed.
The method of adaptive refinement used in OVERFLOW-D is designed to provide resolution of
off-body dynamics associated with complex flow features and/or the motion of body
components. The off-body portion of the domain is defined to encompass the near-body
domain and extend out to the far-field boundaries of the problem. The off- body domain is
filled with overlapping uniform Cartesian grids of variable levels of refinement. All
adaptive refinement takes place within the off-body component grids. Initially, regions of
the off-body field are marked for refinement level based on proximity to near-body
boundaries. However, during the solution process, the off-body field is marked for
refinement level based on estimates of solution error. Subsequent to refinement level
marking (initially and during the solution process), off-body regions of like resolution
are coalesced, or partitioned, into rectilinear blocks of space, each block becoming a
uniform Cartesian grid. Accordingly, at any time during the simulation, the off-body field
is discretized with a set of overlapping uniform Cartesian grid systems of varying levels
of refinement.
Consider an example using the X-38 vehicle.
Near-body grids.
Initial off-body grids.
Solution Error.
Mark off-body field for required refinement level.
Partition off-body domain into blocks requiring like levels of refinement:
Level-1,
Level-2,
Level-3,
Level-4,
Define off-body grids.
Due to the structure of the off-body grid
components used in the approach, OVERFLOW-D is able to exploit numerous computational
advantages of structured data and provides a mechanism for adaptive refinement within the
context of overset structured grids. The method results in large numbers of grid
components, which are automatically organized into groups of near equal size. The grouping
algorithm facilitates efficient use of computer resources and offers a natural mechanism
for group-wise scalability and load balancing. The algorithm distributes problem tasks
equally among a specified number of groups, and attempts to maximize intra-group
satisfaction of intergrid communication requirements, which should lead to good
scalability.
For example, it is anticipated that a 5 million grid point system could be organized into
as many as 100 near uniformly sized groups, and a 25 million grid point system organized
into as many as 500 uniformly sized groups.
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