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17th GAMM-Seminar Leipzig on
Construction of Grid Generation Algorithms

Max-Planck-Institute for Mathematics in the Sciences
Inselstr. 22-26, D-04103 [O->]Leipzig
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  17th GAMM-Seminar
February, 1st-3rd, 2001
 
     
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  Abstract Wolfram Rosenbaum, Sat, 10.00-10.25 Previous Contents Next  
  A Framework for Adaptive Staggered Grids
Wolfram Rosenbaum (Uni Bonn)

Staggered grid schemes are qualified for the approximate solution of hyperbolic systems of conservation laws and operator splitting techniques for transport diffusion problems. On the one hand the ease of evaluating fluxes not on the border but inside a cell, no requirement for (approximate) Riemann solvers and the componentwise application of the scalar framework to solve systems of conservation laws make these schemes very convenient to work with. On the other hand, given a finite element discretization of diffusion on a primal grid a finite volume scheme on the dual grid can easily be modeled to allow the discretization of a simultaneous transport. Besides these obvious advantages there are algorithmical difficulties caused by the use of staggered grids. An especially challenging task, which is particularly important for practical applications, is local adaptive grid-refinement and coarsening, in particular for time dependent phenomena. We have developed a general frame for adaptivity in this context based on adaptive quadtrees and octtrees. Refinement and coarsening is performed on the primal grid only. The corresponding dual grid is defined implicitly based on the primal grid. It is ensured that nodes of the primal grid correspond uniquely to cells in the dual grid. The construction of the adaptive dual grid is completely local. On a primal cell it depends only on the configuration of the primal cell and the adjacent cells. Data access is based on hash tables. The concept has already been worked out in 2D and applied to MHD simulations.
 

 
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Last updated:
30.11.2004 Impressum
 
Concept, Design and Realisation
[O->]Jens Burmeister (Uni Kiel), Kai Helms (MPI Leipzig)
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