Zienkiewicz O.C., Taylor R.L. Vol. 3. The finite - tiera.ru

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¯ow of, 3 ideal, 3, 7, 170 incompressible, 169 Gauss±Legendre integration, 248, 262 Gaussian distribution, 46 Generator: unstructured mesh, 109 structured mesh, 275 Geomechanics, 157 Geometrical factor, 264 Geometry, die, 130 GiD, 289 Gloucester, 229 GLS, 48 Governing equations, depth-averaged, 220 Gradient based procedure, 113 Gradient based re®nement, 110 Gradient procedures, conjugate, 77 Gradients, pressure, 91 Grasho€ Number, 154 Gravity, 91 Gravity forces, 96 Green's theorem, 252, 298 Grids, unstructured, 303 Ground, moving, 192 Group velocity, 243 h-re®nement process, 180 Half-bandwidth, 276, 286 Hankel functions, 256, 258, 260 Harbour: arti®cial o€shore, 258 ¯ow past, 235 Long Beach, 258 open, 250 Harbour series, in®nite, 235 Heat: evolution of, 121 latent, 289 speci®c, 64, 92, 121, 156, 170 Heat capacity, averaged, 159 Heat conduction, 275 Heat convection, 238 Heat ¯ux, conductive, 8 Heat generation terms, 33 Heat input, 124 Heat source terms, 8 Heat transfer, 157 Heat transport equation, 153 Heel angle, 150 Heights, tidal, 227 Helmholtz equation, 223, 242, 243, 244, 248, 255 Hemispheric thrust reverser, 96 Hemker problem, 296 Hermitian matrix, 263 Hexahedra, 132 Hierarchical form, 301 Hierarchical formulation, 300 Hierarchy of boundary operators, 254 High Reynolds number, 113, 207 High-speed ¯ow of gases, 52 High-speed ¯ows, 10, 171, 180, 187, 280 compressible, 280 High-speed gas ¯ow, 169 High-speed vehicles, 212 Higher Mach numbers, 174 Higher-order approximations, 25 Higher-order dampers, 254 Higher-order interpolations, 293 Highly anisotropic di€usion, 28 Hot metals, 120 Hot water discharge, 239 hp re®nements, 103 hp-version ®nite element, 295 Hybrid ®nite element, 295 Hybrid mesh, 204 Hybrid methods, 293 Hydrodynamics: ship, 145, 146 Hydrofoil: submerged, 148, 149 Hydrostatic adjustment, 147 Hydrostatic pressure, 3±5, 223 Hyperbolic duct, 262 Hyperbolic problems, 110 Hypersonic ¯ow, 65, 184, 207 Idea gas law, 7, 170 Ideal ¯ow, 3 Ideal plasticity, 119 Ill-conditioning, 265 Implicit form: fully, 275 nearly, 42, 76 quasi-nearly, 77 Implicit solution, 54 Incident mode, 263 Incident waves, 251, 252 Incompressibility, 1, 2, 3, 5, 10, 11, 66, 78, 81, 97 Incompressible elastic solids, 66, 113 Incompressible ¯ow, 99, 110, 275 CBS algorithm, 97 inviscid, 93 nearly, 10 turbulent, 143 viscous, 113 Incompressible ¯ow codes, 274 Incompressible ¯uid, 218 Incompressible gases, 169 Incompressible laminar ¯ow, 91 Incompressible materials, 92 Subject index 323
324 Subject index Incompressible Stokes ¯ow, 79 Indentation problem, punch, 126 Indirect boundary integral method, 256 In®nite boundaries, 173, 261 In®nite elements, 252, 259, 262, 265 Burnett, 261, 262 conjugated, 264 ellipsoidal type, 261 mapped periodic, 260 static, 260 unconjugated, 264 wave envelope, 262 In®nite harbour series, 235 In®nitesimal strain, 4 In®nity, boundary at, 251 In¯ow boundary, supersonic, 172 In¯ow limits, 178 In¯ow, supercritical, 235 Inlet boundary conditions, 45 Inlet Mach number, 84 Input: data, 275 heat, 124 Inside node, 299 Instability, wave, 271 Insulations, thermal, 157 Intake, engine, 194 Integral method: direct boundary, 255 indirect boundary, 256 Integral models, boundary, 262 Integrals: boundary, 252, 256 domain, 252 exterior boundary, 255 Integration: by parts, 70 direct, 276 Gauss±Legendre, 248, 262 radial, 262 reduced, 116 Interaction, 262 boundary layer, 201 ¯uid-structure, 265, 266 shock, 201 Interface jumps, 294 Interior ¯ows, 169, 172 Intermediate depth water, 268 Intermediate momentum, 279, 284 Internal energy, 170 Internal stresses, 8 Internal work dissipation, 123 Interpolation: local patch, 107 Interpolation error, 104, 106, 108 Interpolation methods, 35 Interpolation of residuals, 301 Interpolations: higher-order, 293 velocity±pressure, 117 Invariant: total strain, 118 Invariants, Riemann, 58 Inviscid behaviour, 171 Inviscid Euler solution, 209 Inviscid examples, three-dimensional, 188 Inviscid ¯ow, 10, 274 Inviscid incompressible ¯ow, 93 Inviscid method, multiblock Euler, 303 Irrotationality, 94 Island problem, arti®cial, 259 Isothermal compressible ¯ow equations, 223 Isothermal conditions, 177 Isothermal ¯ow, 178 Isothermal form, 219 Isotropic ¯uid, linear newtonian, 5 Isotropic meshes, 109 Isotropic thermal conductivity, 8 Isotropic, viscosity, 118 Iterations, Newton±Raphson, 130 Iterative convergence, 188 Iterative non-linear solution, 96, 147 Jet, axisymmetric, 96 Jump: positive, 235 Jumps, interface, 294 Keel, 150, 153 Kinematic condition, 265, 266 Kinematic viscosity, 66, 154, 162 Kinetic energy, 121 turbulent, 162 Korteweg±de Vries equation, 268 Kronecker delta, 5, 65 Kutta±Joukoski condition, 150 Lag-entrainment, 210, 303, 304 Lagrange multipliers, 294 Lagrangian velocity increment, 132 LameÂ notation, 5 Laminar ¯ow, 210, 302 incompressible, 91 Laminar ¯ows, 210 Lapidus-type arti®cial di€usion, 179, 180 Laplace's equation, 96, 265, 266 Laplacian form, 97 Large eddy simulation (LES), 161 Large wave height, 245 Large-amplitude progressive waves, 268 Large-amplitude water waves, 265, 266 Latent heat, 289
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The Finite Element Method Fifth edi
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The Finite Element Method Fifth edi
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Dedication This book is dedicated t
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3.7 The performance of two- and sin
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Volume 2: Solid and structural mech
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xiv Preface to Volume 3 this algori
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2 Introduction and the equations of
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10 Introduction and the equations o
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12 Introduction and the equations o
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14 Convection dominated problems We
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16 Convection dominated problems wh
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18 Convection dominated problems ch
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20 Convection dominated problems i.
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22 Convection dominated problems 2
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24 Convection dominated problems 2.
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26 Convection dominated problems ar
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28 Convection dominated problems Th
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30 Convection dominated problems co
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32 Convection dominated problems 2.
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34 Convection dominated problems ha
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36 Convection dominated problems an
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38 Convection dominated problems ac
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40 Convection dominated problems An
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42 Convection dominated problems U
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44 Convection dominated problems (a
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46 Convection dominated problems sp
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48 Convection dominated problems ag
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50 Convection dominated problems To
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52 Convection dominated problems C
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56 Convection dominated problems an
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60 Convection dominated problems Ma
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62 Convection dominated problems 47
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3 A general algorithm for compressi
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66 A general algorithm for compress
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92 Incompressible laminar ¯ow Cons
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94 Incompressible laminar ¯ow and,
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96 Incompressible laminar ¯ow V/V
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98 Incompressible laminar ¯ow The
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100 Incompressible laminar ¯ow 1.5
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102 Incompressible laminar ¯ow p 1
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104 Incompressible laminar ¯ow �
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106 Incompressible laminar ¯ow x 2
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108 Incompressible laminar ¯ow Thi
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114 Incompressible laminar ¯ow (a)
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116 Incompressible laminar ¯ow (b)
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118 Incompressible laminar ¯ow wit
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120 Incompressible laminar ¯ow The
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122 Incompressible laminar ¯ow Fig
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124 Incompressible laminar ¯ow and
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126 Incompressible laminar ¯ow U U
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128 Incompressible laminar ¯ow C L
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130 Incompressible laminar ¯ow are
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132 Incompressible laminar ¯ow sha
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134 Incompressible laminar ¯ow Fig
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136 Incompressible laminar ¯ow 28.
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138 Incompressible laminar ¯ow 71.
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140 Incompressible laminar ¯ow 114
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142 Incompressible laminar ¯ow 153
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144 Free surfaces, buoyancy and tur
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170 Compressible high-speed gas ¯o
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7 Shallow-water problems 7.1 Introd
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220 Shallow-water problems reduced
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222 Shallow-water problems Approxim
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224 Shallow-water problems These si
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226 Shallow-water problems h = 2 η
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228 Shallow-water problems Surface
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230 Shallow-water problems FL: 578
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232 Shallow-water problems B Fig. 7
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234 Shallow-water problems Time = 0
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236 Shallow-water problems Fig. 7.1
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238 Shallow-water problems where no
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240 Shallow-water problems 14. T.D.
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8 Waves Peter Bettess 8.1 Introduct
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244 Waves the familiar form where
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246 Waves of 10 nodes or thereabout
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248 Waves and the Astley wave envel
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250 Waves agreement with the analyt
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252 Waves Fig. 8.3 General wave dom
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254 Waves Relative errors (%) 10 8
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256 Waves (The indirect boundary in
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258 Waves where m is the number of
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260 Waves Fig. 17.6 of Volume 1. La
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262 Waves to using such coordinate
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264 Waves r/a 5 4 3 2 1 0 0 2 4 6 8
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266 Waves 8.16 Three-dimensional ef
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268 Waves wave elevations in shallo
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270 Waves integrals. Preliminary re
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Page 287 and 288: 9 Computer implementation of the CB
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Page 305 and 306: 292 Appendix A Again substituting t
Page 307 and 308: 294 Appendix B As usual the domain
Page 309 and 310: 296 Appendix B 5. While the piecewi
Page 311 and 312: Appendix C Edge-based ®nite elemen
Page 313 and 314: Appendix D Multigrid methods It is
Page 315 and 316: Appendix E Boundary layer±inviscid
Page 317 and 318: 304 Appendix E In Fig. E.2, Cp is t
Page 320 and 321: Author index Page numbers in bold r
Page 322 and 323: Gerdes, K. 259, 264, 265, 272 Ghia,
Page 324 and 325: Nakos, D.E. 146, 165 Narayana, P.A.
Page 326: Wu, J. 67, 90; 102, 108, 112, 137;
Page 329 and 330: 316 Subject index Blurring of the s
Page 331 and 332: 318 Subject index Convected coordin
Page 333 and 334: 320 Subject index Elements ± cont.
Page 335: 322 Subject index Flows: buoyancy d
Page 339 and 340: 326 Subject index Metals: hot, 120
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Page 343 and 344: 330 Subject index Shock interaction
Page 345 and 346: 332 Subject index Theorem ± cont.
Page 347: 334 Subject index Wave ± cont. ste
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