FINITE VOLUME METHOD – POWERFUL MEANS OF ENGINEERING DESIGN docx

FINITE VOLUME METHOD – POWERFUL MEANS OF ENGINEERING DESIGN Edited by Radostina Petrova Finite Volume Method – Powerful Means of Engineering Design Edited by Radostina Petrova Published by InTech Janeza Trdine 9, 51000 Rijeka, Croatia Copyright © 2012 InTech All chapters are Open Access distributed under the Creative Commons Attribution 3.0 license, which allows users to download, copy and build upon published articles even for commercial purposes, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. After this work has been published by InTech, authors have the right to republish it, in whole or part, in any publication of which they are the author, and to make other personal use of the work. Any republication, referencing or personal use of the work must explicitly identify the original source. As for readers, this license allows users to download, copy and build upon published chapters even for commercial purposes, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. Notice Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published chapters. The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained in the book. Publishing Process Manager Romana Vukelic Technical Editor Teodora Smiljanic Cover Designer InTech Design Team First published March, 2012 Printed in Croatia A free online edition of this book is available at www.intechopen.com Additional hard copies can be obtained from orders@intechopen.com Finite Volume Method – Powerful Means of Engineering Design, Edited by Radostina Petrova p. cm. ISBN 978-953-51-0445-2 Contents Preface IX Part 1 Different Aspects in FVM, New Techniques and Algorithms 1 Chapter 1 Application of Finite Volume Method in Fluid Dynamics and Inverse Design Based Optimization 3 Árpád Veress and József Rohács Chapter 2 Numerical Schemes for Hyperbolic Balance Laws – Applications to Fluid Flow Problems 35 Marek Brandner, Jiří Egermaier and Hana Kopincová Chapter 3 Use of Proper Closure Equations in Finite Volume Discretization Schemes 61 A. Ashrafizadeh, M. Rezvani and B. Alinia Chapter 4 The Complete Flux Scheme for Conservation Laws in Curvilinear Coordinates 83 J.H.M. ten Thije Boonkkamp and M.J.H. Anthonissen Chapter 5 An Alternative Finite Volume Discretization of Body Force Field on Collocated Grid 101 Jure Mencinger Chapter 6 Alternative Methods for Generating Elliptic Grids in Finite Volume Applications 117 A. Ashrafizadeh, M. Ebrahim and R. Jalalabadi Chapter 7 The Finite Volume Method in Computational Rheology 141 A.M. Afonso, M.S.N. Oliveira, P.J. Oliveira, M.A. Alves and F.T. Pinho Part 2 Studies of Particular Problems Through FVM, Development of New Ways for Their Solution 171 Chapter 8 Rayleigh–Bénard Convection in a Near-Critical Fluid Using 3D Direct Numerical Simulation 173 Accary Gilbert VI Contents Chapter 9 A Concept of Discretization Error Indicator for Simulating Thermal Radiation by Finite Volume Method Based on an Entropy Generation Approach 199 H. C. Zhang, Y. Y. Guo, H. P. Tan and Y. Li Chapter 10 Volume-of-Fluid (VOF) Simulations of Marangoni Bubbles Motion in Zero Gravity 215 Yousuf Alhendal and Ali Turan Chapter 11 Mass Conservative Domain Decomposition for Porous Media Flow 235 Jan M. Nordbotten, Eirik Keilegavlen and Andreas Sandvin Chapter 12 On FVM Transport Phenomena Prediction in Porous Media with Chemical/Biological Reactions or Solid-Liquid Phase Change 257 Nelson O. Moraga and Carlos E. Zambra Chapter 13 Finite Volume Method for Streamer and Gas Dynamics Modelling in Air Discharges at Atmospheric Pressure 283 Olivier Ducasse, Olivier Eichwald and Mohammed Yousfi Part 3 Application of FVM in Medicine and Engineering 307 Chapter 14 Conjugate Gradient Method Applied to Cortical Imaging in EEG/ERP 309 X. Franceries, N. Chauveau, A. Sors, M. Masquere and P. Celsis Chapter 15 Wood Subjected to Hygro-Thermal and/or Mechanical Loads 327 Izet Horman, Dunja Martinović, Izet Bijelonja and Seid Hajdarević Chapter 16 Integrated Technology for CAD Modeling and CAE Analysis of a Basic Hydraulic Cylinder 347 Radostina Petrova and Sotir Chernev Preface Beginner or advanced learner, young or old, student or experienced scientist, we hope that after reading this introduction you will find a topic which will raise your interest and engage your thought to further investigate a problem and to build on the presented work. Finite Volume Method (FVM) is among the most powerful means for solving different engineering problems. It is used in fluid mechanics, meteorology, electromagnetics, semi-conductor device simulation, models of biological processes and many more engineering applications. This book addresses a wide variety of concepts in FVM. Therefore, it is almost impossible to classify precisely or to outline the boundaries of all presented works. They are result of the efforts of scientists from all over the world. However, without having any pretense, just in order to help you, all book chapters are systemized in the following three general groups: Works studying different aspects of FVM and suggesting new techniques and algorithms, all validated through already proven examples. In the first chapter a study of the application of FVM in computational fluid dynamics and inverse design based optimization can be found. The authors describe and validate their ideas through test examples. Another chapter focusses on the applications of numerical schemes for hyperbolic balance laws in fluid flow problems. Its authors do not aim to make a detailed comparison of all presented methods; their intention is the chapter be accepted as a partial guide on choosing the most appropriate numerical approach for solving nonhomogeneous hyperbolic partial differential equations through FVM. To illustrate the properties of some of the described methods several numerical examples for urethra flow and for shallow water flow are provided. The complete flux scheme for conservation laws in curvilinear coordinates is also discussed in the book. The equations of numerical flux for Cartesian, for spherical and for cylindrical coordinates are given. The authors investigate the aspects of time integration considering the derivation to time-dependent conservation laws. X Preface According to the author of “An Alternative Finite Volume Discretization of Body Force Field on Collocated Grid”, collocated grids are more suitable for implementation on general geometries than the staggered counterparts. He proposes discretization on collocated grids, which does not change the solution substantially and could generally be used. The following aspects of the problem are discussed: weak pressure-velocity coupling, staggered versus collocated grids, corrections of convecting velocity. The proposed alternative body force discretization against the standard discretization for moving fluid is tested in two cases: raise of a bubble in a rectangular cavity and natural convection in a square cavity. In chapter “Alternative Methods for Generating Elliptic Grids in Finite Volume Applications” classical elliptic grid generation (EGG methods) is reviewed and a classification is made. The authors propose unified view, providing a framework for the development of new grid generation methods, which are introduced here for the first time. Some of the presented methods are computationally cheaper than the existing ones and provide grids with comparable qualities. All grid generation examples are limited to two dimensional solution domains, but the underlying ideas are clearly applicable in three-dimensional problems as well. A new scheme, Method of Proper Closure Equations (MPCE), for successful solution to incompressible and compressible flow problems is proposed in the next chapter. Discussion on different available schemes and on the building blocks of MPCE is presented through one-dimensional test cases, but MPCE are also applicable on 2D structured or unstructured grids. The answer of the question why the FVM should be as successful as finite element method in computational rheology is given in “The Finite Volume Method in Computational Rheology”. The authors summarize contributions and methodologies related to the description of different flows (creeping, viscoelastic), stating that stability, convergence and accuracy have always been intimately related to the development of FVM in CR. They focus on FVM, applied to viscoelastic fluids using collocated meshes. In addition, some high-resolution schemes, formulation of the mass fluxes at cell faces and formulation of the cell-face stresses are discussed. The solution is provided through time-marching version of SIMPLEC algorithm, including few new steps related to the stress calculation. Works studying particular problems through FVM and establishing new ways for their solution In chapter “Rayleigh–Bénard Convection in a Near-critical Fluid Using 3D Direct Numerical Simulation”, the author considers a cell containing supercritical fluid (SCF) in a cube-shaped cavity, subjected to the earth gravity. His investigation relies on a mathematical model, based on equations governing near-critical fluid buoyant flows and implementing acoustic filtering. Several aspects of Rayleigh-Bénard convection in a near-critical fluid are given. A comparison between the Rayleigh-Bénard convection . FINITE VOLUME METHOD – POWERFUL MEANS OF ENGINEERING DESIGN Edited by Radostina Petrova Finite Volume Method – Powerful Means of Engineering Design Edited. to eliminate the influence of the turbulent fluctuations, meanwhile the unsteadiness of the other physical Finite Volume Method – Powerful Means of Engineering Design 6 phenomenon are. refer to the complete system of equations beside momentum, including both mass and energy conservation laws. Finite Volume Method – Powerful Means of Engineering Design 4 scale to be much