Project Title:
Fuzzy Grid Methods for Computational Fluid Dynamics
02.01-1515
910919
Fuzzy Grid Methods for Computational Fluid Dynamics
Cambridge Hydrodynamics, Inc.
P.O. Box 1403
Princeton
NJ
08542
Ilya
Staroselsky
609-683-1515
ARC
NAS2-13514
009
02.01-1515
910919
Abstract:
Fuzzy Grid Methods for Computational Fluid Dynamics
Grid generation for computational fluid dynamics (CFD) is a critically important
field of technology. The fuzzy grid method is a novel way to generate simple and
robust unstructured grids for the solutions of equations in very complex geometries.
In comparison with the current state-of-the-art unstructured grid methods such as
Delaunay/Voronoi grids, fuzzy grids are easier to apply to higher dimensional problems
and have better stability properties. Many of the most important research questions
today in computational fluid dynamics involve strongly inhomogeneous velocity fields,
compressible turbulent flows, and shock waves. Such occurrences are found in regions
of relatively smooth velocity fields interspersed with regions of high vorticity
and high pressure gradients. This causes conventional structured grid techniques
such as spectral element methods to be very wasteful in terms of computer time and
storage. Unstructured grid techniques are a more efficient approach but have proven
difficult to implement in high dimensions. Also, the complexity induced by the nonlocal
interactions in the grid makes the analysis of their mathematical properties difficult.
This innovative fuzzy grid technique is easy to implement on both vector and parallel
supercomputers and its simplicity enables mathematical verification of important
stability and convergence properties.
The development of efficient, easy-to-use software is key to enabling the accurate,
efficient solution of complex engineering problems in many areas. The fuzzy grid
technique will have commercial interest because it will allow robust, accurate simulations
of the most complex flows of industrial interest.
grid generation, unstructured grid, Voronoi grid, Delaunay tringulation, nearest
neighbor algorithms, CFD, parallel computing