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Experiences with a space–time multigrid method for the optimal control of a chemical turbulence model
Author(s) -
Borzì Alfio,
Griesse R.
Publication year - 2005
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.904
Subject(s) - multigrid method , turbulence , space (punctuation) , lambda , reaction–diffusion system , diffusion , mathematics , optimal control , statistical physics , mathematical optimization , physics , computer science , mathematical analysis , mechanics , partial differential equation , thermodynamics , optics , operating system
Abstract Lambda–omega systems provide a universal model to investigate two‐species reaction diffusion problems. In the case of fast reaction kinetics and small diffusion, these systems evolve to turbulent behaviour. A class of open‐loop optimal control problems governed by lambda–omega systems in the turbulent regime is investigated. Optimal solutions are characterized by optimality systems consisting of two pairs of reaction diffusion equations with opposite time orientation. These systems are solved by a space–time multigrid scheme suitable for the turbulent setting. Numerical examples are given where the control drives the chaotic system to form regular patterns. Copyright © 2005 John Wiley & Sons, Ltd.