Decomposition Methods in Multiphysics and Multiscale Problems: Models and Simulation (Physics Research and Technology)

Jürgen Ernst Geiser

ISBN 10: 1617286117 / ISBN 13: 9781617286117

Published by Nova Science, 2012

About this Item

Hardcover, xi + 183 pages, NOT ex-library. A clean and bright copy with unmarked text and firm binding, free of inscriptions and stamps. Published without a dust jacket. -- Contents: 1 Introduction 2 Analytical and Numerical Solutions for Convection-Diffusion-Dispersion-Reaction Equations with General Initial-Conditions: Theory and Applications [Mathematical Model; Time and Spatial Decomposition Methods; Discretization; Analytical Solutions; Numerical Experiments (Transported Triangle (One-Dimensional Problem); Rotating Pyramid; Realistic Simulations); Conclusions and Discussions] 3 Modified Operator Splitting Methods and Applications to Pathway Models [Mathematical Model (Transport Model; Pathway Model); Decomposition Method (Accelerated Iterative Operator Splitting Methods; Analytical Examples for Iterative Splitting Methods); Experiment for the Sputter Process (Benchmark Problem 1; Benchmark 2: 2 x 2 Matrix; Sputter Reactions: Experiment 1; Experiment 3: Realistic Example (10 x 10)); Conclusions and Discussions; Appendix] 4 Embedded Linearization Techniques for an Iterative Splitting Method and Application to a Model for Particle Transport [Mathematical Model for Kinetic Problems; Operator Splitting Methods as Code Coupling Schemes (Time Dependent Iterative Splitting Method; Linearization Schemes for the Time Dependent Iterative Scheme); Experiment for the Plasma Reactor (Test-Example: Bernoulli Equation (n=3) & General Bernoulli Equation with n = 9 & Convection-Diffusion-Reaction Equation with Non-linear Reaction; Simplified Model for the Collision Process in the Plasma Reactor)] 5 Transport and Chemical Reaction: Characteristics Method and Splitting Methods [Mathematical Model; Discretization and Solver Methods (Finite Volume Methods; Numerical Solution of the Advection Equation; Analytical Solution to a System of Ordinary Differential Equations of First Order; Numerical Methods for ODEs; Computation of Mass Conservation); Splitting Methods (First Order for Linear Equations (A-B-Splitting); Iterative Splitting Method; Iterative Splitting Method with Embedded Multigrid Methods; Prolongation and Restriction Operators; Iterative Solvers: Waveform Relaxation); Numerical Experiments: Microscopic Models (One Dimensional Particle Model: Reaction Model; Heavy Particle Model: Transport Model; Heavy-Particle Model (One-Dimensional Velocity)); Appendix (Matlab Commands & Codes)] 6 Operator-Splitting Methods via Zassenhaus PFormula [Operator Splitting Methods; Higher Order Operator Splitting Methods (Classical Operator Splitting Errors; Higher order A-B splitting by Initialization; Higher Order A-B-A Splitting by Accelerating the Subproblems via Weighted Polynomials; Higher Order A-B-A Splitting Based on Zassenhaus Product Formula; Higher Order Iterative Splitting Based on Zassenhaus Product Formula); Extended Splitting Method Based on Zassenhaus-Formula; Balancing of Time and Spatial Discretization; Improved Iterative Splitting Method by Embedded Zassenhaus-Formula; Numerical Examples; Appendix: Zassenhaus Product Formula] 7 Iterative Operator Splitting Methods for Navier Stokes: Molecular Dynamics Simulation [Mathematical Model; Iterative Splitting Method; Molecular-Level Shear Stress Computation; Numerical Results (Time-Dependent Channel Flow Simulation; Dual-Time Stepping Method with Viscosity Averaging)] 8 Outlook; Literature; Index.

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Bibliographic Details

• Title: Decomposition Methods in Multiphysics and Multiscale Problems: Models and Simulation (Physics Research and Technology)
• Publisher: Nova Science
• Publication Date: 2012
• Language: English
• ISBN 10: 1617286117
• ISBN 13: 9781617286117
• Binding: Hardcover
• Condition: Near Fine

About this title

Synopsis

This book models chemical vapour deposition (CVD) for metallic bipolar plates and simulates the deposit of a homogeneous layer. Also discussed herein are mesoscopic models, which reflect the transport and reaction of the gaseous species through a homogeneous media in the chamber. The models include the conservation of mass and the porous media in accordance with Darcy's law. The transport through the stationary and non-ionised plasma field is treated as a diffusion-dominated flow, where the metallic deposit and the gas chamber look like porous media. This book examines the theoretical results of decomposition methods, as well as presents the application to the CVD apparatus.