Adaptive multiresolution schemes with local time stepping for two- dimensional degenerate reaction-diffusion systems

Details

Serval ID
serval:BIB_0184198748EF
Type
Article: article from journal or magazin.
Collection
Publications
Title
Adaptive multiresolution schemes with local time stepping for two- dimensional degenerate reaction-diffusion systems
Journal
Applied Numerical Mathematics
Author(s)
Bendahmane M., Bürger R., Ruiz-Baier R., Schneider K.
ISSN-L
0168-9274
Publication state
Published
Issued date
2009
Peer-reviewed
Oui
Volume
59
Pages
1668-1692
Language
english
Abstract
Spatially two-dimensional, possibly degenerate reaction-diffusion systems, with a focus on models of combustion, pattern formation
and chemotaxis, are solved by a fully adaptive multiresolution scheme. Solutions of these equations exhibit steep gradients, and in the degenerate case, sharp fronts and discontinuities. This calls for a concentration of computational effort on zones of strong variation.
The multiresolution scheme is based on finite volume discretizations with explicit time stepping.
The multiresolution representation of the solution is stored in a graded tree ("quadtree"), whose leaves are the non-uniform finite
volumes on whose borders the numerical divergence is evaluated. By a thresholding procedure, namely the elimination of leaves with Solution values that are smaller than a threshold value, substantial data compression and CPU time reduction is attained. The threshold value is chosen such that the total error of the adaptive scheme is of the same order as that of the reference finite volume scheme.
Since chemical reactions involve a large range of temporal scales, but are spatially well localized (especially in the combustion model), a locally varying adaptive time stepping strategy is applied. For scalar equations, this strategy has the advantage that consistence with a CFL condition is always enforced. Numerical experiments with five different scenarios, in part with local time stepping, illustrate the effectiveness of the adaptive multiresolution method. It turns out that local time stepping accelerates the adaptive multiresolution method by a factor of two, while the error remains controlled. (C)
2008 IMACS.
Keywords
Degenerate parabolic equation, Adaptive multiresolution, scheme, Pattern formation, Finite volume schemes, , Chemotaxis, Kellerâeuro"Segel systems, Flame balls, interaction, Locally varying time stepping
Create date
02/07/2013 9:54
Last modification date
20/08/2019 12:23
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