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.

purchase the full-text of this chapter (price £20)

go to the previous chapter
go to the next chapter
return to the table of contents
return to the book description
purchase this book (price £95 +P&P)