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A Critical Study of Agglomerated Multigrid Methods for DiffusionAgglomerated multigrid techniques used in unstructured-grid methods are studied critically for a model problem representative of laminar diffusion in the incompressible limit. The studied target-grid discretizations and discretizations used on agglomerated grids are typical of current node-centered formulations. Agglomerated multigrid convergence rates are presented using a range of two- and three-dimensional randomly perturbed unstructured grids for simple geometries with isotropic and highly stretched grids. Two agglomeration techniques are used within an overall topology-preserving agglomeration framework. The results show that multigrid with an inconsistent coarse-grid scheme using only the edge terms (also referred to in the literature as a thin-layer formulation) provides considerable speedup over single-grid methods but its convergence deteriorates on finer grids. Multigrid with a Galerkin coarse-grid discretization using piecewise-constant prolongation and a heuristic correction factor is slower and also grid-dependent. In contrast, grid-independent convergence rates are demonstrated for multigrid with consistent coarse-grid discretizations. Actual cycle results are verified using quantitative analysis methods in which parts of the cycle are replaced by their idealized counterparts.
Document ID
20090024830
Acquisition Source
Langley Research Center
Document Type
Conference Paper
Authors
Thomas, James L. (NASA Langley Research Center Hampton, VA, United States)
Nishikawa, Hiroaki (National Inst. of Aerospace Hampton, VA, United States)
Diskin, Boris (National Inst. of Aerospace Hampton, VA, United States)
Date Acquired
August 24, 2013
Publication Date
June 22, 2009
Subject Category
Fluid Mechanics And Thermodynamics
Report/Patent Number
LF99-9040
AIAA Paper 2009-4138
Meeting Information
Meeting: 19th AIAA Computational Fluid Dynamics
Location: Texas
Country: United States
Start Date: June 22, 2009
End Date: June 25, 2009
Sponsors: American Inst. of Aeronautics and Astronautics
Funding Number(s)
WBS: WBS: 736466.11.01.07.43.01.02
Distribution Limits
Public
Copyright
Public Use Permitted.

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