Computational fluid dynamics principles and applications j blazek

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COMPUTATIONAL FLUID DYNAMICS: PRINCIPLES AND APPLICATIONS J Blazek ELSEVIER Computational Fluid Dynamics: Principles and Applications Elsevier Science Internet Homepage http://www.elsevier.nl (Europe) http://www.elsevier.com (America) http://www.elsevier.co.jp (Asia) Consult the Elsevier homepage for full catalogue information on all books journals and electronic producu and services Elsevier Tte of Related Interest ils Computational Fluids and Solid Mechanics Ed K-JBathe ISBN: 008-0439446 The Mathematics of Finite Elements and Applications X Ed J.R Whiteman ISBN: 0084435688 AF'COM '99 - 4* Asia Pacific Conference on Computational Mechanics Ed K.H Lee ISBN: 0080432093 Related Journals Free specimen copy gladly senr on request Elsevier Science md,The Boulevard, Lungford Lane Kidlingion, O.rford, OX5 IGB UK Advances in Engineering Software Computer Methods in Applied Mechanics and Engineering Computers and Fluids Computers and Structures Engineering Analysis with Boundary Elements Finite Elements in Analysis and Design International Journal of Heat and Mass Transfer Probabilistic Engineering Mechanics To Contact the Publisher Elsevier Science welcomes enquiries concerning pubIishing proposals: books, journal special issues, conference proceedings, etc All formats and media can be considered Should you have a publishing proposal you wish to discuss please contact, without obligation, the publisher responsible for Elsevier's numerical methods in engineering programme: Dr James Milne Publisher, Engineering and Technology Elsevier Science Ltd The Boulevard, Langford Lane Idlington, Oxford OX5 1GB UK Phone: Fax: Email: +44 1865 843891 +44 1865843920 j.mihe@elsevier.co.uk General enquiries, including placing orders should be directed to Elsevier's Regional Salts Officcs - please access the Elsevier homepage for full contact details (homepage details at the top of this page) Computational Fluid Dynamics: Principles and Applications J Blazek Alstom Power Ltd., Baden-Daettwil, Switzerland 200 ELSEVIER - Amsterdam London New York Oxford * Pans * Shannon Tokyo ELSEVIER SCIENCE Ltd The Boulevard, Langford Lane Kidlington, Oxford OX5 IGB, UK @ J 2001 J Blazek All rights reserved This work is protected under copyright of Blazek with assigned rights to Elsevier Science The following terms and conditions apply to its use: Photocopying Single photocopiesof single chaptersmay be made for personal use as allowed by national copyright laws Permission of the Publisher and payment of a fee is required for all other photocopying, including multiple or systematic copying, copying for advertising or promotional putposcs, resale, and all forms of document delivery Special rates are available for educational institutions that wish to make photocopiesfor non-profit educationalclassroom use Permissions may be sought directly from Elsevier Science Global Rights DepartmenS PO Box 800, Oxford OX5 IDX, U K phone: (+44) 1865 843830, fax: (+44) 1865 853333,e-mail: permissions@elsevier.co.uk.You may also contact Global Rights directly through Elsevier‘s home page (http://www.elsevier.nl), hy selecting ‘Obtaining Permissions’ In the USA, users may clear permissions and make payments through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923,USA; phone: (+I) (978)7508400,fax: (+I) (978)7504744,and in the UK through thecopyright Licensing Agency Rapid Clearance Service (CLARCS), 90 Tottenham Court Road, London WIP OLP, UK, phone: (+44) 207 63 5555; fax: (+44)207 63 5500 Other countries may have a local reprographicrights agency for payments Derivative Works Tables of contents may be reproduced for internal circulation, but permission of Elsevier Science is required for external resale or distribution of such material Permission of the Publisher is required for all other derivative works, including compilationsand translations Electronic Storage or Usage Permission of the Publisher is required to store or use electronically any material contained in this work, including any chapter or part of a chapter Except as outlined above no part of this work may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior written permission of the Publisher Address permissions requests to: Elsevier Science Global Rights Department, at the mail, fax and e-mail addresses noted above Notice No responsibilityis assumed by the Publisher for any injury and/or damage to persons or property as a matter of products liability negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein Because of rapid advances in the medical sciences, in particular, independentverification of diagnoses and drug dosages should be made First edition 2001 Library of Congress Cataloging in Publication Data A catalog record from the Library of Congress has been applied for British Library Cataloguing in Publication Data Blazek, J Computational f l u i d dynamics : p r i n c i p l e s and a p p l i c a t i o n s P l u i d dynamics - Computer s i m u l a t i o n P l u i d dynamics Mathematical models 1.Title - 532’.05 ISBN 0080430090 ISBN: 08 043009 @ The paper used in this publication meets the requirements of ANSIMISO 239.484992 (Permanence of Paper) Printed in The Netherlands V Contents Acknowledgements xi List of Symbols xiii Abbreviations xix Introduction Governing Equations 2.1 The Flow and its Mathematical Description 2.2 Conservation Laws 2.2.1 The Continuity Equation 2.2.2 The Momentum Equation 2.2.3 The Energy Equation 2.3 Viscous Stresses 2.4 Complete System of the Navier-Stokes Equations 2.4.1 Formulation for a Perfect Gas 2.4.2 Formulation for a Real Gas 2.4.3 Simplifications to the Navier-Stokes Equations Bibliography 5 Principles of Solution of the Governing Equations 3.1 Spatial Discretisation 3.1.1 Finite Difference Method 3.1.2 Finite Volume Method 3.1.3 Finite Element Method 3.1.4 Other Discretisation Methods 3.1.5 Central versus Upwind Schemes 3.2 Temporal Discretisation 3.2.1 Explicit Schemes 3.2.2 Implicit Schemes 3.3 Turbulence Modelling 3.4 Initial and Boundary Conditions Bibliography 8 10 13 16 18 19 22 26 29 32 36 37 39 40 41 45 46 49 53 56 58 vi Contents Spatial Discretisation: Structured Finite Volume Schemes 4.1 Geometrical Quantities of a Control Volume 4.1.1 Two-Dimensional Case 4.1.2 Three-Dimensional Case 4.2 General Discretisation Methodologies 4.2.1 Cell-Centred Scheme 4.2.2 Cell-Vertex Scheme: Overlapping Control Volumes 4.2.3 Cell-Vertex Scheme: Dual Control Volumes 4.2.4 Cell-Centred versus Cell-Vertex Schemes 4.3 Discretisation of Convective Fluxes 4.3.1 Central Scheme with Artificial Dissipation 4.3.2 Flux-Vector Splitting Schemes 4.3.3 Flux-Difference Splitting Schemes 4.3.4 Total Variation Diminishing Schemes 4.3.5 Limiter Functions 4.4 Discretisation of Viscous Fluxes 4.4.1 Cell-Centred Scheme 4.4.2 Cell-Vertex Scheme Bibliography 75 79 79 80 83 83 85 88 91 93 95 98 105 108 110 116 118 119 120 Spatial Discretisation: Unstructured Finite Volume Schemes 129 5.1 Geometrical Quantities of a Control Volume 134 5.1.1 Two-Dimensional Case 134 5.1.2 Three-Dimensional Case 135 5.2 General Discretisation Methodologies 138 5.2.1 Cell-Centred Scheme 139 5.2.2 Median-Dual Cell-Vertex Scheme 142 5.2.3 Cell-Centred versus Median-Dual Scheme 146 5.3 Discretisation of Convective Fluxes 150 5.3.1 Central Schemes with Artificial Dissipation 150 5.3.2 Upwind Schemes 154 5.3.3 Solution Reconstruction 154 5.3.4 Evaluation of Gradients 160 5.3.5 Limiter Functions 165 5.4 Discretisation of Viscous Fluxes 169 5.4.1 Element-Based Gradients 169 171 5.4.2 Average of Gradients Bibliography 174 Temporal Discretisation 6.1 Explicit Time-Stepping Schemes 6.1.1 Multistage Schemes (Runge-Kutta) 6.1.2 Hybrid Multistage Schemes 6.1.3 Treatment of the Source Term 6.1.4 Determination of the Maximum Time Step 6.2 Implicit Time-Stepping Schemes 181 182 182 184 185 186 190 Coiiteiits 6.2.1 Matrix Form of Implicit Operator 6.2.2 Evaluation of the Flux Jacobian 6.2.3 AD1 Scheme 6.2.4 LU-SGS Scheme 6.2.5 Newton-Krylov Method 6.3 Methodologies for Unsteady Flows 6.3.1 Dual Time-Stepping for Explicit Multistage Schemes 6.3.2 Dual Time-Stepping for Implicit Schemes Bibliography vii 191 195 199 202 208 212 213 215 216 Turbulence Modelling 225 7.1 Basic Equations of Turbulence 228 7.1.1 Reynolds Averaging 229 7.1.2 Favre (Mass) Averaging 230 7.1.3 Reynolds-Averaged Navier-Stokes Equations 231 7.1.4 Favre- and Reynolds-Averaged Navier-Stokes Equations 232 7.1.5 Eddy-Viscosity Hypothesis 233 7.1.6 Non-Linear Eddy Viscosity 235 7.1.7 Reynolds-Stress Transport Equation 236 7.2 First-Order Closures 238 7.2.1 Spalart-Allmaras One-Equation Model 238 7.2.2 K-a Two-Equation Model 241 7.2.3 SST Two-Equation Model of Menter 245 7.3 Large-Eddy Simulation 248 7.3.1 Spatial Filtering 249 7.3.2 Filtered Governing Equations 250 7.3.3 Subgrid-Scale ModelliIig 252 7.3.4 Wall Models 255 Bibliography 256 Boundary Conditions 267 8.1 Concept of Dummy Cells 268 270 8.2 Solid Wall 8.2.1 Inviscid Flow 270 8.2.2 Viscous Flow 275 277 8.3 Fafield 8.3.1 Concept of Characteristic Variables 277 8.3.2 Modifications for Lifting Bodies 279 8.4 Inlet/Outlet Boundary 283 8.5 Symmetry Plane 285 8.6 Coordinate Cut 286 8.7 Periodic Boundaries 287 8.8 Interface Between Grid Blocks 290 8.9 Flow Gradients at Boundaries of Unstructured Grids 293 Bibliography 294 Appendix 433 [I41 Koobus, B.; Farhat, C.: Time-Accurate Schemes for Computing Two- and Three-Dimensional Viscous Fluxes on Unstructured Dynamic Meshes INRIA Report No 2833, March, 1996 [15] Koobus, B.; Farhat, C.: Second-Order Schemes that Satisfy the GCL for Flow Computations on Dynamic Grids AIAA Paper 98-0113, 1998 [16] Venkatakrishnan, V.; Mavriplis, D.J.: Implicit Method for the Computation of Unsteady Flows on Unstructured Grids J Computational Physics, 127 (1996), pp 380-397 [17] Steger, J.L.: Implicit Finite Difference Simulation of Flows About Arbitrary Geometries AIAA Journal 17 (1978) 679-686 [18] Pulliam, T.H.; Steger, J.L.: Implicit Finite Difference Simulations of 3-0 Compressible Flows AIAA Journal 18 (1980) 159-167 [19] Pa,tankar, S.V.; Spalding, D.B.: A Calculation Procedure for Heat, Mass and Momentum Transfer in Three-Dimensional Parabolic Flows Int J Heat Mass Transfer, 15 (1972), pp 1787-1806 [20] Pulliam, T.H.; Steger, J.L.: Recent Improvements i n Eficiency, Accurucy, and Convergence for Implicit Approzimate Factorization Algorithms AIAA Paper 85-0360, 1985 [21] Warming, R.F.; Beam, R.; Hyett, B.J.: Diagonalization and Simultaneous Symmetrization of the Gas-Dynamic Matrices Math Comp., 29 (1975), p 1037 [22] Whitham, G.B.: Linear and Nonlinear Waves Wiley, New York, 1974 [23] Saad, Y ; Schulz, M.H.: GMRES: A Generalized Minimum Residual Algorithm for Solving Nonsymmetric Linear Systems SIAM J Scientific and Statistical Computing, (1986), pp 856-869 Index ADI: Alternating Direction Implicit, 50, 199,366 Advancing-front Delaunay, 367 Advancing-front method, 367, 373 Advancing-layers method, 376 Advancing-normal point placement, 379 Agglomeration multigrid, 316 Algebraic grid generation, 356, 359 Algebraic models, 55 All-speed Aow, 320 AMG: Algebraic Multigrid, 305, 315 Amplification factor, 335 Approximate Riemann solver, 43,105 Arrhenius formulae, 22 ARS: Algebraic Reynolds Stress, 54 Artificial compressibility method, 30, 320 Artificial dissipation, 41, 95, 150 AUSM: Advection Upstream Splitting Method, 42, 98, 101 Average of fluxes, 83, 88, 139, 142 Average of variables, 83, 88, 139, 145 Carbuncle phenomenon, 107 Cartesian grids, 29, 381 Cell-centred scheme, 37, 76, 83, 132, 139 Cell-vertex scheme, 37, 78, 85, 88, 132, 142 Central scheme, 41, 95, 150 Centrifugal force, 411 CFL condition, 186, 338, 347, 348 CFL number, 183, 186,338,347 CGS: Conjugate Gradient Squared, 51, 208 Characteristic boundary conditions, 56 Characteristic time-stepping, 47 Characteristic variables, 42, 106,109, 115, 277,424 Characteristics of PDE’s, 407 Chimera technique, 34, 290 Circulation, 280 CIRS: Central Implicit Residual Smoothing, 301 Co-located grid scheme, 78 Coarse grid correction, 307 Computational molecule, 93 Computational space, 32, 356 Condition number, 320 Conjugate gradient method, 51,208 Conservation laws, Conservative variables, 16, 78 Consistency, 331, 332 Constrained Delaunay triangulation, 372 Containment-dual control volume, 146 Continuum, Contravariant velocity, 16, 414 Control functions, 363 Background grid, 368 Backscatter, 252 Baldwin-Lomax model, 55 Bi-CGSTAB: Bi-Conjugate Gradient Stabilised, 51, 208 Body-fitted grid, 29 Boundary conditions, 56 Boussinesq hypothesis, 54, 233 Bradshaw’s assumption, 246 Bubble packing method, 367 Bulk viscosity, 15 435 Index 436 Control volume, 79, 80, 134, 135 Convective flux Jacobian, 419 Convective flux tensor, Convective fluxes, 6, 16, 93, 150 Coordinate cut, 286, 357, 359 Coriolis force, 411 Curvilinear grid, 32 CUSP: Convective Upwind Split Pressure, 42, 98, 103 Cyclic directions, 292 Dalton’s law, 21 Damkohler number, 19 Damping functions, 241, 243 Damping properties, 334 Decoupling, 95, 118, 171 Degrees of freedom, 39 Delaunay method, 367, 368 Density (mass) weighted decomposition, 53, 230 Density-based schemes, 30 Dependent variables, 78 Determinant of Jacobian of coordinate transformation, 404 Differential form, 401 Diffusive flux, Diffusive flux tensor, Dilatation, 15 Direct methods, 49, 191 Dirichlet tessellation, 368 Discretisation accuracy, 333 Discretisation error, 331 DNS: Direct Numerical Simulation, 53, 225 Domain decomposition, 34 Dual control volumes, 37, 78, 88, 142 Dual time-stepping approach, 49,212 Dummy cells, 268 Dummy points, 268 Dynamic SGS models, 254 Dynamic viscosity coefficient, 13 Eddy viscosity, 55, 225, 233 Edge collapsing, 316 Eigenvalue, 106, 108, 425, 426 Eigenvector, 106, 109, 424426 Einstein summation convention, 431 Elliptic grid generation, 356, 363 ENO: Essentially Non-Oscillatory, 43 Ensemble averaging, 230 Enthalpy, 18 Enthalpy damping, 300 Entropy condition, 38 Entropy correction, 108, 109 Equation of state, 18 Ergodic hypothesis, 230 Euler equations, 25 Explicit operator, 190 Explicit scheme, 182 Explicit time-stepping scheme, 46 External body forces, External volume forces, Face vector, 79-81, 135-137 Factored scheme, 191 Factorisation error, 50, 201 FAS: Full Approximation Storage, 48,306 Favre (mass) averaging, 53, 230 Favre decomposition, 53, 230 Finite control volume, Finite difference method, 32, 36 Finite element method, 32, 39 Finite volume method, 32, 37 First-order closures, 54, 225, 238 Fluctuation-splitting scheme, 42,43 Fluid dynamics, Flux, Flux Jacobian, 32, 42, 47, 49, 190, 191, 195 Flux-difference splitting scheme, 42, 43, 105 Flux-vector splitting scheme, 42, 98 FMG: Full Multigrid, 48, 309 Forcing function, 306 Fourier symbol, 335 Frontal Delaunay, 367 Gauss’s theorem, 40 Gaussian filter, 249 Index GCL: Geometric Conservation Law, 17,213,415 German0 identity, 254 Global coarsening, 317 Global time stepping, 187 GMRES: Generalised Minimal Residual, 51, 208, 427 Green-Gauss gradient computation, 160, 293 Grid cells, 29 Grid converged solution, 41, 333 Grid generation, 29 Grid lines, 29 Grid nodes, 29 Grid points, 29 Grid refinement, 316 Grid smoothing, 383 Grid vertices, 29 Gridless Method, 40 H-CUSP scheme, 104 Hanging nodes, 32 High Reynolds number model, 245 Horse-shoe vortex, 279 Hybrid grids, 32, 129, 379 Hyperbolic grid generation, 356,365 IGES: Initial Graphics Exchange Specification, 353 ILU: Incomplete Lower Upper, 51, 210 Implicit operator, 49, 190, 191, 305 Implicit scheme, 190 Implicit time-stepping scheme, 46, 49 Implicit-explicit residual smoothing, 47 Incremental point insertion, 369 Inflow, Integral formulation, Internal energy, 10 Interpolation operator, 306 IRS: Implicit Residual Smoothing, 47,301 Tterative methods, 50, 191 Jacobi preconditioning, 47 437 Jacobian coordinate transformation, 37 Jacobian matrix, 419, 421 JST scheme, 96 K-w model, 55 K-E model, 55, 241 Kinematic eddy viscosity, 229 Kinematic viscosity coefficient, 15 Kronecker symbol, 431 Krylov subspace, 50, 208 Laplacian operator, 151, 383 LDFSS: Low-Diffusion Flux-Splitting Scheme, 42, 98 Least-squares gradient computation, 162 Left state, 43, 84, 90, 93, 140 Left/right preconditioning, 51, 210 LES: Large-Eddy Simulation, 53,248 Limiter, 44, 94, 110, 165 Limiter for CUSP scheme, 114 Limiter for TVD scheme, 115 Limiter function, 44, 94, 110, 165 Line-implicit methods, 50 Linear reconstruction, 157 Linear TFI, 362 Linelets, 50 Local time-stepping, 46, 187 Low Reynolds number model, 241 LU-SGS: Lower-Upper Symmetric GaussSeidel, 50, 202 LU-SSOR: Lower-Upper Symmetric Successive Overrelaxation, 50, 202 Lumped mass matrix, 45, 182, 190 MAPS: Mach Number-Based Advcction Pressure Splitting, 42, 98 Mass matrix, 45, 181, 190, 212, 214 Matrix dissipation scheme, 42, 98, 153 Matrix-free approach, 51, 209 Max-min triangulation, 367 Median-dual control volume, 132,142 438 Mesh, 29 Method of lines, 30,45, 75, 129, 181 Method of weighted residuals, 39 Metric terms, 404 Metrics, 79, 134 Mixed grids, 32, 129, 367, 379 Monotonicity preserving scheme, 43, 110, 165 Morkovin’s hypothesis, 53, 232 Multiblock approach, 32, 290 Multigrid cycle, 47 Multigrid level, 47 Multigrid method, 47, 305 Multiphase flow, 22 Multistage scheme, 182 Multistage time-stepping scheme, 46 MUSCL: Monotone Upstream-Centred Schemes for Conservation Laws, 94, 111, 155 Navier-Stokes equations, 17 Newton-Krylov method, 52,191,208, 210 Newtonian fluid, 13 Non-linear eddy viscosity, 55, 235 Nonnested grids, 316 Normal-momentum relation, 270 Noslip boundary condition, 57, 275 NURBS: Non-Uniform Rational BSplines, 378 Order of accuracy, 36, 333 Outflow, Overlapping control volumes, 37,78, 85, 132 Overrelaxation parameter, 204, 206, 208 Perfect gas, 18 Periodic boundary, 359 Phase angle, 335 Physical space, 29 Piecewise linear prolongation, 319 PNS: Parabolised Navier-Stokes, 23, 409, 418 Point implicit, 186 Index Prandtl number, 19, 55, 234, 403 Preconditioning, 30, 320 Preconditioning matrix, 321 Pressure sensor, 97 Pressure-based schemes, 30, 320 Prolongation operator, 307 Pseudo-Laplacian, 151 Quadratic reconstruction, 158 RANS: Reynolds-Averaged NavierStokes, 53, 231 RCM: Reverse Cuthill-McKee, 195, 210 Real gas, 19, 44 Reconstruction, 133, 139, 145, 150, 154, 160 Reflected cells, 285 Residual, 45, 76, 132, 181 Residual averaging, 47 Residual distribution, 86 Residual smoothing, 47, 301 Restriction operator, 306 Reynolds averaging, 53, 229 Reynolds-stress tensor, 54, 231, 232 Right state, 43, 84, 90, 93, 140 Roe average, 106 Roe matrix, 106 Roe scheme, 43, 106 Rotating frame of reference, 17,411 Rotation-rate tensor, 228 Rotational periodicity, 287, 289 Rothalpy, 412 Rotor-stator interaction, 380 RST: Reynolds-Stress Transport, 54, 236 Runge-Kutta time-stepping scheme, 46, 182 Scalar dissipation scheme, 96 Search directions, 51, 209 Second viscosity coefficient, 13 Second-order closures, 54, 225 Seed points, 317 Semicoarsening, 306 SGS: Subgrid-Scale stress, 250 Index Shape functions, 39 Sharp Fourier cut-off filter, 249 Single-stage time-stepping scheme, 46 Singletons, 317 SLIP: Symmetric Limited Positive, 96 Slope limiter, 111 Smagorinsky SGS model, 253 Smooth grid, 29, 131 Solution reconstruction, 139, 145,150, 154, 160 Solution update, 181 Source term, 76, 131, 185, 190 Spalart-Allmaras model, 55, 238 Spatial averaging, 229 Spatial discretisation, 32, 76, 131 Spectral Element Method, 40 Spectral radius, 97, 153, 187-189 Stability, 331 Stability analysis, 334 Staggered grid scheme, 78 Steger-Warming flux-vector splitting, 195 Steiner point, 372 Stencil, 93 Stiffness, 185, 190 Stokes’s hypothesis, 403 Strain-rate tensor, 228 Structured grids, 32, 356 Structurcd scheme, 75 Subgrid-scale model, 53, 248, 252 Surface forces, Surface grid, 356 Surface grid generation, 379 Sutherland formula, 18 Switched Evolution Relaxation, 211 Symmetric TVD scheme, 43, 108 System matrix, 190, 305 439 Thermal diffusivity coefficient, 7, 11 Time averaging, 229 Time step, 186 Time-stepping operator, 335 Tophat filter, 249 Total energy, 10, 411 Total enthalpy, 12, 412 Translational periodicity, 287 Truncation error, 36, 332 TSL: Thin Shear Layer, 23,119,199, 416 Turbulence modelling, 53, 225 Turbulent dissipation rate, 236 Turbulent eddy viscosity, 55, 233 Turbulent heat-flux vector, 54, 233, 234 Turbulent kinetic energy, 231, 232 Turbulent Prandtl number, 55, 234 Turbulent thermal conductivity coefficient, 55, 234 TVD: Total Variation Diminishing, 42, 43, 108 Two-equation models, 241 UIRS: Upwind Implicit Residual Smoothing, 47, 303 Unit normal vector, 6, 16, 77, 7981, 134, 135, 137, 140, 144, 244,412,414 Unsteady flows, 49, 212 Unstructured grids, 32, 34, 367 Unstructured scheme, 129 Upwind prolongation, 310, 314, 316 Upwind restriction, 310, 316 Upwind scheme, 42, 154 Upwind TVD scheme, 43, 108, 109 V-Cycle, 308 Validation, 332 Van Albada limiter, 111 Van Leer’s flux-vector splitting, 99 Tensor notation, 228,431 Variational principle, 39 TFI: Transfinite Interpolation, 356, Vector of convective fluxes, 16 359 TFQMR: Transpose-Free Quasi-Minimum Vector of viscous fluxes, 16 Verification, 332 Residual, 51, 208 Virtual edges, 164 Thermal conductivity coefficient, 11 440 Viscous flux Jacobian, 199, 421 Viscous fluxes, 16, 116, 169 Viscous stress tensor, 9, 228 Viscous stresses, 13 Visibility criterion, 378 Volume agglomeration, 317 Volume grid, 356 Von Neumann stability analysis, 334 Voronoj diagram, 368 Vortex correction, 280, 281 W-Cycle, 308 Wall functions, 245 Weak formulation, 39 Weak solutions, 38 Index COMPUTATIONAL FLUID DYNAMICS: PRINCIPLES AND APPLICATIONS Computational Fluid Dynamics (CFD) is an important design tool in engineering and also a substantial research tool in various physical sciences The objective of this book is to provide a solid foundation for understanding the numerical methods employed in today’s CFD and to raise awareness of modern CFD codes through hands-on experience The book will be an essential reference work for engineers and scientists starting to work in the field of CFD or those who apply CFD codes The accompanying CD-ROM contains the sources of 1-D and 2-D Euler solvers as well as grid generators Chapters Introduction Governing Equations Principles of Solution of the Governing Equations Spatial Discretisation: Structured Finite Volume Schemes Spatial Discretisation: Unstructured Finite Volume Schemes Temporal Discretisation Turbulence Modelling Boundary Conditions Acceleration Techniques 10 Consistency, Accuracy and Stability 11 Principles of Grid Generation 12 Description of the Source Codes ISBN 08 043009 Front cover image courtesy of Brodersen, DLR, Germany ... (homepage details at the top of this page) Computational Fluid Dynamics: Principles and Applications J Blazek Alstom Power Ltd., Baden-Daettwil, Switzerland 200 ELSEVIER - Amsterdam London New York... books journals and electronic producu and services Elsevier Tte of Related Interest ils Computational Fluids and Solid Mechanics Ed K-JBathe ISBN: 008-0439446 The Mathematics of Finite Elements and. .. Mechanics and Engineering Computers and Fluids Computers and Structures Engineering Analysis with Boundary Elements Finite Elements in Analysis and Design International Journal of Heat and Mass

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