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

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Estuary: Severn, 226±236 Euler boundary conditions, 305 Euler equation, 8±10, 93, 150, 171±177, 218, 298, 302 Euler ¯ow, 83, 148 Euler problems, 180 Euler solution, 192 inviscid, 209 pure, 209 Euler±Stokes equations, 275 Eulerian ¯ow modelling, 212 Evolution of heat, 121 Exit, ¯ow, 293 Expansion: Taylor, 39, 40 Experiments, physical, 169 Explicit algorithm, 100 Explicit characteristic±Galerkin procedure, 38, 40 Explicit dynamic codes, 132 Explicit form, 76, 275, 284 Explicit method, direct, 175 Explicit mode, fully, 99 Explicit scheme, 43 Explicit semi-explicit, 76 Explicit time marching algorithm, 104 Exponential law, 118 Exterior acoustics, 261 Exterior boundaries, 173 Exterior boundary integrals, 255 Exterior ¯ows, 169, 172 Exterior problems, 252, 253 Exterior region, 256 Exterior series solutions, 255 Exterior solutions, 253 linking to, 255 Exterior surface wave problems, 250 Exterior wave problems, 251 External boundaries, 172, 227 Extremum, local, 176 Extrusion, 121, 122 transient, 128 Feeder, 144 FEM, wave envelope, 264 Fictitious boundary, 81, 172 Fighter, supersonic, 189 Filling of moulds, 143, 145, 148 Fine ®nite element mesh, 300 Finite di€erences, 2 one-sided, 17 Finite element: Galerkin, 176 hp-version, 295 hybrid, 295 special, 249 Subject index 321 Finite increment calculus (FIC), 25, 30 Finite volume formulation, 189 First-order closure models, 162 First-order di€raction problem, 268 Flat nosed punch, 129 Floating body, 265, 266 Floating breakwater, 265, 266, 267 Flooding, 231 Flow: compressible, 10, 48, 50, 66, 108, 170, 174, 224, 275 Euler, 83, 148 high speed, 169, 171, 180 hypersonic, 184, 207 ideal, 3 incompressible, 110, 275 incompressible laminar, 91 incompressible Stokes, 79 inviscid, 10 inviscid incompressible, 93 isothermal, 178 Mach 3, 187 mass, 6 potential, 3, 93 pure Stokes, 98 shallow water, 219, 50 steady-state, 120 Stokes, 2, 91, 118 subsonic, 81, 84, 189 supercritical, 236 supersonic, 185 transonic viscous, 203 turbulent, 164, 275, 289 viscous incompressible, 113 Flow codes, incompressible, 274 Flow coupling, boundary layer-inviscid, 302 Flow-dependent viscosity, 3 Flow equations: averaged, 162 isothermal compressible, 223 potential, 146 Flow exit, 293 Flow ¯uxes, mass, 92 Flow formulation, 120 Flow modelling, Eulerian, 212 Flow of gases, 3 Flow past a cylinder, 161 Flow past harbour, 235 Flow problems: compressible viscous, 274 ¯uid, 110 high-speed, 280 inviscid, 274 Flow separation, 171, 245 Flow vector, mass, 74
322 Subject index Flows: buoyancy driven, 153, 156 compressible, 73, 91, 173, 218, 280 high-speed, 280 exterior, 169, 172 free surface, 3, 91, 144 high-speed, 10, 187 hypersonic, 65 incompressible, 91 interior, 169, 172 laminar, 210 nearly incompressible, 10 non-newtonian, 118 porous media, 274, 276, 286 shallow water, 3 slow, 113 super critical, 235 supersonic, 82 thermal, 286 turbulent, 161, 210, 274 turbulent incompressible, 143 viscoelastic, 131 Fluid: Bingham, 118 incompressible, 218 non-newtonian, 91 stresses in, 4 Fluid density, 6 Fluid dynamic, 4 Fluid dynamics, 1 Fluid ¯ow problems, 110 Fluid±structure interaction, 265, 266 Fluid±structure, submarine, 262 Fluidized beds, packed and, 157 Flux: average, 294 conductive heat, 8 mass ¯ow, 92 Flux conservation, complete, 293 Flux matrices, 13 Flux quantities, di€usive, 14 Forced convection, 144, 286 Forces: boundary, 91 buoyancy, 91 convective, 55 Coriolis, 229 driving, 154 gravity, 96 perturbation, 144 prescribed, 55 second-order wave, 271 wave, 250 Forces due to breaking, 235 Forchheimer Number, 159 Forming: metal, 2, 3, 118, 120, 122 polymer, 118 sheet, 122 superplastic, 130 transient metal, 132 Free boundary condition, 233 Free surface, 96, 143±145, 219, 265, 266, 274 Free surface ¯ows, 3, 91, 144 Free wave, 269 Frequency independent mass matrix, 265 Frequency: angular, 242, 243 Friction: bed, 226, 235, 245 skin, 202 Friction coe cient: Manning, 229 skin, 304 Frictional dissipation, 228 Frictional resistance, 226 Front, shock, 196 Froude Number, 148, 149, 224, 235, 236 Fully conservative form, 286 Fully explicit form, 76, 275 Fully explicit mode, 99 Fully implicit form, 275 Fully incompressible problems, 99 Function: convected shape, 37 linear shape, 16 oscillatory, 262 potential, 94 Functional, 251 energy, 255 Functions: Hankel, 256, 258, 260 trignometric, 256, 260 vector-valued, 52 velocity trial, 223 weighting, 19 Galerkin algorithm, characteristic, 43 Galerkin approximation, 54, 57, 70 (See also Bubnov±Galerkin, Petrov±Galerkin) Galerkin ®nite element, 18, 176 Galerkin Least Squares (GLS), 30 Galerkin methods, 1, 16, 23 characteristic, 34 discontinuous, 293 Galerkin, discontinuous, 26 Gas constant: universal, 7, 65, 154, 170 Gas ¯ow: compressible, 57, 73, 218 high-speed, 57, 169 gas, compressible, 169
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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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Page 287 and 288: 9 Computer implementation of the CB
Page 289 and 290: 276 Computer implementation of the
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: 320 Subject index Elements ± cont.
Page 337 and 338: 324 Subject index Incompressible St
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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