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COMPUTATIONAL METHODS FOR ENGINEERING TECHNOLOGY
Edited by: B.H.V. Topping and P. Iványi
Multi-Scale Methods for Transport Problems: Theory and Applications
Department of Physics, University of Greifswald, Germany
J. Geiser, "Multi-Scale Methods for Transport Problems: Theory and Applications", in B.H.V. Topping and P. Iványi, (Editor), "Computational Methods for Engineering Technology", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 7, pp 157-190, 2014. doi:10.4203/csets.35.7
Keywords: multi-scale methods, transport problems, deterministic–stochastic splitting, iterative splitting, multi-scale spitting.
In recent years, multi-scale methods for transport problems have played an increasingly important role in the numerical solution of stochastic and deterministic partial differential equations. Multi-scale strategies are particularly important to embed scale-dependent information between the micro- and macro-models. Based on the ideas of matching, seaming and averaging, we discuss methods, such as: heterogeneous multi-scale method, equation free method and multi-scale iterative splitting method. This review paper presents the latest research results in multi-scale splitting methods of high accuracy, efficiency and effectiveness. Multi-scale methods for transport problems will be investigated for important engineering and physics applications. The paper reviews the different multi-scale methods for transport problems, which are applied, and we concentrate on discussing: (1) Theory of the well known multi-scale methods; (2) Splitting methods as multi-scale solvers; and (3) Engineering applications in computational fluid-dynamics problems based on deterministic and stochastic differential equations.
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