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

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Diagonal term: lower, 80 stabilizing, 78 Die geometry, 130 Dielectric constant, 243 Di€raction, 250, 251 elastic sphere, 262 ellipse, 261 wave, 248, 250 Di€raction problem, ®rst-order, 268 Di€usion, 4, 238 arti®cial, 22 balance, 20, 22, 27 convective, 34, 36 cross-wind, 29 highly anisotropic, 28 Lapidus-type arti®cial, 179 negative, 22 stabilizing, 39 streamline balancing, 28 Di€usion coe cient, 14, 237 arti®cial, 175 Di€usion conduction coe cient, 293 Di€usion error, 239 Di€usion terms, 25, 38, 237 Di€usive ¯ux quantities, 14 Di€usive terms, 50 viscous, 76 Di€usivity: arti®cial, 50, 224 thermal, 154 Dirichlet boundary conditions, 293, 294 Dirichlet to Neumann (DtN) mapping, 253 Discharge of hot ¯uid, 238, 239 Discontinuity, 50 sharp, 181 Discontinuous Galerkin, 26, 293 Discretization: mixed, 116 penalty, 116 spatial, 70 Dispersal, pollutant, 218, 227 Dispersion relation, 243, 269, 271 Displacement thickness, 304 Dissipation: arti®cial, 174 energy, 8 frictional, 228 internal work, 123 viscous, 245 Dissipation terms, 286 Distribution: gaussian, 46 pressure, 211 Domain integrals, 252 Domain subdivision, unstructured, 2 Domains, general wave, 252 Double ellipsoid, 207, 208 Drag stresses, bottom, 222 Drag: viscous, 146 wind, 221 Drawing: deep, 122, 129 Drift angle, 150 Driven cavity problem, 115 Driven convection, buoyancy, 161 Driven ¯ows: buoyancy, 153, 156 Driving force, 154 Drying areas, 236 DtN algorithm, 253, 259 Duct, hyperbolic, 262 DYNA3D, 132 Dynamic codes, explicit, 132 Dynamic equilibrium, 6 Dynamic shear viscosity, 5 Dynamic viscosity, 66, 156 Ebbing, 231 Eddies, 161, 245 Eddy shedding, 3 Eddy viscosity, turbulent, 162 Edge formulation, 212 Edge: trailing, 150 Edge-based ®nite element formulation, 298 Eigenvalue analysis, 58, 244 Eigenvectors, 244 Elastic behaviour, 2 Elastic bulk modulus, 11 Elastic compressibility, 132 Elastic recovery, 132 Elastic solids, incompressible, 66 Elastic sphere di€raction, 262 Elastic waves, 245 Elasticity, incompressible, 113 Electric ®eld intensity vectors, 246 Electromagnetic scattering problems, 246 Electromagnetic wave problems, 57 Electromagnetic waves, 4, 242, 243, 245 Electromagnetics, 243, 250 (See also ®nite element) Elements: Burnett, 262 conjugated in®nite, 264 elongated, 197 ®nite, 2 in®nite, 252, 259, 265 linear triangular, 283 quadrilateral, 206, 207 special ®nite, 249 Subject index 319
320 Subject index Elements ± cont. static in®nite, 260 structured triangle, 206 tetrahedral, 206 triangle, 207, 274 unconjugated in®nite, 264 Element area calculation, 276 Element elongation, 107, 108, 109 Element formulation, edge-based ®nite, 298 Element grids, structured ®nite, 274 Element size, smallest, 181 Element stretching, 182 in®nite, 262 potential, 265, 266 Elements grids, unstructured ®nite, 274 Elementwise conservative, 296 Elevation: second-order wave, 269 total wave, 251 wave, 242, 243 Elevations: tidal, 226 wave, 265, 266 Ellipse di€raction, 261 Ellipsoid: double, 207, 208 Ellipsoidal coordinates, 261, 262 Ellipsoidal type in®nite elements, 261 Elongated elements, 197 Elongation directions, 180 Elongation: element, 107±109 Energy, 159, 170, 284 balance of, 8 conservation of, 66, 92, 291 internal, 170 kinetic, 121 speci®c, 92, 94 turbulent kinetic, 162 Energy conservation, 7, 65, 124 Energy conservation equation, 3 Energy coupling, 279 Energy dissipation, 8 Energy equation, 74, 91, 286, 289 Energy functional, 255 Energy norm error, 113 Energy transport, 11 Energy/temperature calculation, 279 Engine intake, 194 Enthalpy, 8, 94 Entrainment coe cient, 304 Entropy, constant, 64 Equation of state, 7, 67 Equation solving, 275 Equation: Bernoulli, 94, 147, 265, 266 Burger, 50, 52 continuity, 99 convection±di€usion, 4, 26, 47, 293 density-pressure, 73 energy, 74, 286, 289 energy conservation, 3 Euler, 9, 176, 177 heat transport, 153 Helmholtz, 223, 242, 243, 244, 248, 255 Korteweg±de Vries, 268 Laplace, 96, 265, 266 momentum, 154 Navier±Stokes, 9 Poisson, 97 pure convection, 146 scalar convection±di€usion, 92 self-adjoint, 96 transport, 14, 163 wave, 242 Equations: averaged ¯ow, 162 convection±di€usion, 13, 25, 72 decoupled, 58 depth-averaged governing, 220, 237 energy, 91 Euler, 8, 10, 93, 150, 171, 172, 218, 298, 302 Euler±Stokes, 275 Maxwell, 243, 246 Navier±Stokes, 10, 26, 146, 150, 170, 180, 197, 210, 212, 219, 291 non-conservative, 9 non-self-adjoint, 1 potential ¯ow, 146 shallow-water, 223 Stokes, 81 transient scalar, 34 transport, 171 wave, 268 Equations of motion, 153 Equilibrium conditions, 304 Equilibrium, dynamic, 6 Ergun's relations, 159 Error estimator, 102 Error indicator, 102 Error indicators, a posteriori, 244 Error limit, 106 Error: di€usion, 239 energy norm, 113 interpolation, 104, 106, 108 pollution, 244 RMS departure, 106 Errors, phase, 229 Estimator, error, 102 Estuaries, coastal, 218
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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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...................................
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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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Page 283 and 284: 270 Waves integrals. Preliminary re
Page 285 and 286: 272 Waves 39. R.J. Astley. FE mode
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: 318 Subject index Convected coordin
Page 335 and 336: 322 Subject index Flows: buoyancy d
Page 337 and 338: 324 Subject index Incompressible St
Page 339 and 340: 326 Subject index Metals: hot, 120
Page 341 and 342: 328 Subject index Prescribed tracti
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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Zienkiewicz O.C., Taylor R.L. Vol. 3. The finite - tiera.ru

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