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2005, 2005(Special): 11-21. doi: 10.3934/proc.2005.2005.11

Multiscale methods for advection-diffusion problems

Assyr Abdulle 1,

1. 

Mathematica Department, University of Basel, Rheinsprung 21, CH-4051 Switzerland

Received  September 2004 Revised  April 2005 Published  September 2005

The development of numerical methods for multiscale advection-diffusion problems presents a number of challenges. The one-scale structures may significantly in uence the coarser properties of the system, but are often impossible to solve in full details. The time integration of the evolution system is still due to the diffusion term and its stability properties have to be taken into account for its resolution. We discuss in this paper an algorithm, which combines Heterogeneous Multiscale Methods (HMM) with Orthogonal Runge-Kutta Chebyshev (ROCK) methods, for the efficient numerical resolution of multiscale advection-diffusion problems.
Keywords: homogenization., heterogeneous multiscale methods, ROCK methods, sti problems, multiscale advection di usion problems.
Mathematics Subject Classification: 65N30, 65L20, 74Q05; Secondary:74Q15,7430.
Citation: Assyr Abdulle. Multiscale methods for advection-diffusion problems. Conference Publications, 2005, 2005 (Special) : 11-21. doi: 10.3934/proc.2005.2005.11
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