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2016 | Buch

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Multicomponent and Multiscale Systems

Theory, Methods, and Applications in Engineering

verfasst von: Juergen Geiser

Verlag: Springer International Publishing

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This book examines the latest research results from combined multi-component and multi-scale explorations. It provides theory, considers underlying numerical methods and presents brilliant computational experimentation. Engineering computations featured in this monograph further offer particular interest to many researchers, engineers and computational scientists working in frontier modeling and applications of multicomponent and multiscale problems. Professor Geiser gives specific attention to the aspects of decomposing and splitting delicate structures and controlling decomposition and the rationale behind many important applications of multi-component and multi-scale analysis. Multicomponent and Multiscale Systems: Theory, Methods and Applications in Engineering also considers the question of why iterative methods can be powerful and more appropriate for well-balanced multiscale and multicomponent coupled nonlinear problems. The book is ideal for engineers and scientists working in theoretical and applied areas.

Inhaltsverzeichnis

Frontmatter

Chapter 1. General Principles

Abstract

In the general principle, we give an overview of the recently used methods and schemes to solve multicomponent and multiscale systems. While multicomponent systems are evolution equations based on each single species, which are coupled with the other species, e.g. with reaction-, diffusion-processes, multiscale systems are evolution equations based on different scales for each species, e.g. macroscopic- or microscopic scale. We give the general criteria for practically performing the different splitting and multiscale methods, such that a modification to practical applications of the splitting schemes to a real-life problem can be done.

Juergen Geiser

Chapter 2. Theoretical Part: Functional Splitting

Abstract

We describe a general method, which is based on a splitting approach and the knowledge of the exact solutions of some sub-problems. Such additional information is taken into account and has an important role in accelerating the computations. We apply a functional splitting idea to decompose the initial problem into several sub-problems where some of them are known with the analytical solutions. The sub-problems with unknown solutions are solved numerically by standard numerical methods, e.g. finite volume methods. This paper can be divided into four parts. In the first part, we introduce the model and its application. In the second part, we discuss the analytical solutions of coupled systems of convection-reaction equations. Functional splitting methods are developed in the third part.

Juergen Geiser

Chapter 3. Algorithmic Part

Abstract

In this chapter, we discuss the algorithmic parts with respect to the different methods we applied in the application part.

Juergen Geiser

Chapter 4. Models and Applications

Abstract

In this section, we discuss the different multicomponent and multiscale models, which are later applied in simulations. We focus on the coupling of microscopic and macroscopic models, while the microscopic model is related on finer spatial and time scales and the macroscopic model is related to the coarser spatial and time scales. We discuss exemplary engineering problems in the field of electronic application and transport reaction applications in Plasma models. Here, the models and their underlying multiscale and multicomponent methods are discussed. Based on the aligned methods, we see the data flow between the disparate scales and can estimate the accuracy in each micro- and macroscopic model, such that we obtained truly working multiscale and multicomponent approaches.

Juergen Geiser

Chapter 5. Engineering Applications

Abstract

In this chapter, we discuss the different engineering applications related to multicomponent and multiscale models, that occur in different categories (microscopic, mesoscopic and macroscopic). As we have described in the Introduction on p. xxv. That such models can be used as basic model to couple to more complicate models, describing materials, interfaces, etc., see Rosso and de Baas (Review of materials modelling: what makes a material function? Let me compute the ways, 2014, [1]).

Juergen Geiser

Backmatter

Titel: Multicomponent and Multiscale Systems
verfasst von: Juergen Geiser
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-15117-5
Print ISBN: 978-3-319-15116-8
DOI: https://doi.org/10.1007/978-3-319-15117-5

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