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

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Law: conservation, 13 exponential, 118 idea gas, 3, 170 plasticity, 132 Sutherland's, 171 Lawrence Livermore Laboratory, 132 Lax±Wendro€, 246 Layer: sponge, 254 Leaking lid formulation, 97 Leibnitz rule, 220 Lid-driven cavity, 100, 101, 103, 104, 111 Linear newtonian isotropic ¯uid, 5 Linear shape function, 16 Linear triangular elements, 283 Linking to boundary integrals, 255 Linking to exterior solutions, 255 Linking to series solutions, 256 Local extremum, 176 Local non-re¯ecting boundary conditions, 253 Local patch interpolation, 107 Local time stepping, 78, 280, 284 Localizing shocks, 181 Locally structured mesh, 108 Locked wave, 269 Locking, 132 Long Beach harbour, 258 Long-wave propogation, 224 Longshore currents, 235 Low Mach number, 65, 81, 84, 173 Low Rayleigh number, 159 Low Reynolds number models, 163 Lower diagonal term, 80 Lumped mass, 42, 43, 78, 175, 177, 278, 284 M2 tide, 227 M6 wing: ONERA, 208, 209 Mach 2, 189, 194, 204 Mach 3 ¯ow, 187 Mach 8.15, 207 Mach contours, 208 Mach number, 110, 169, 172, 188, 199, 204, 276, 304 higher, 174 inlet, 84 low, 81, 84 lower, 173 Magnetic ®eld intensity vectors, 246 Manning friction coe cient, 229 Mapped periodic in®nite elements, 260 Mapping, DtN, 259 Mass: conservation of, 1, 6, 64, 66, 91, 219, 242, 291 Mass ¯ow, 6, 74, 92 Mass, lumped, 78 Mass matrices, 244 consistent, 175, 177, 284 lumped, 175, 177, 284 Mass matrix calculation, 278, 284 Mass matrix: consistent, 43, 298 frequency independent, 265 lumped, 43 Mass transfer, 274, 275 Mass transport, 289 Material code, 275 Materials, incompressible, 92 Matrices: conditioning of system, 250 consistent mass, 43, 175, 177, 284, 298 diagonal, 58, 72 ¯ux, 13 hermitian, 263 lumped mass, 43, 175, 177, 284 mass, 244 positive de®nite, 295 sti€ness, 244, 256 Maximum principal curvatures, 108 Maxwell equations, 243, 246 Mean water level, 219 Media ¯ows: porous, 274, 276, 286 Medium, porous, 157 Melenk and BabusÆ ka method, 247 Mesh: adaptive, 205 ®ne, 300 hybrid, 204 isotropic, 109 locally structured, 108 moving, 122 structured, 169, 207, 276, 286 surface, 152 uniform, 112 unstructured, 286 updated, 36 Mesh data, 275 Mesh enrichment, 113, 180, 181 Mesh generation: adaptive, 113 anisotropic, 109 structured, 275 unstructured, 109 Mesh re®nement, 110, 113 adaptive, 102 Mesh solution, coarse, 300 Mesh subdivisions, 301 Mesh updating, 35, 147 Metal forming, 2, 3, 118 transient, 132 Subject index 325
326 Subject index Metals: hot, 120 Meteorology, 218, 223 Method: (See also algorithms, procedures, process) characteristic±Galerkin, 34±36, 68, 176 direct explicit, 175 direct solution, 169 discontinuous Galerkin, 293 explicit characteristic±Galerkin, 40 Galerkin, 23 hybrid, 293 interpolation, 35 lag-entrainment, 210 multigrid, 300 Petrov±Galerkin, 18, 33 pseudo-concentration, 148 residual based, 176 shock capture, 174 Taylor±Galerkin, 34 Thwaites compressible, 303 two-step predictor±corrector, 55 wave envelope, 246 Minimum curvatures, 109 Minimum step, 280 Mixed and penalty formulations, 113 Mixed convection, 286 Mixed discretization, 116 Mixed form, 116 Mixing length, Prandtl, 163 Mode: fully explicit, 99 incident, 263 spiral, 264 Models: boundary integral, 262 Boussinesq, 162 computational, 251 DARPA submarine, 149, 152 ®rst-order closure, 162 -!, 163, 164 one-equation, 162 transpiration velocity, 210 turbulent -", 209 turbulent -!, 209 turbulence, 212 two-equation, 163 Modulus: bulk, 5, 11, 64, 91, 92, 242 shear, 5, 115 Momentum, 159, 162, 304 balance of, 6 conservation of, 66, 92, 291 intermediate, 279 Momentum balance, 242 Momentum calculations, intermediate, 284 Momentum conservation, 6, 65, 219 Momentum correction, 279 Momentum equation, 154 Momentum variables, 284 Monochromatic plane wave, 252 Mont St Michel, 236 Motion: convective, 157 equations of, 153 ship, 145 Motor car, 192 Mould ®lling, 143±148 Moving ground, 192 Moving mesh, 122 Multiblock Euler inviscid method, 303 Multidimensional problems, 15 Multigrid, 188, 189, 212, 300 Multiple wave directions, 247 Multiple wave speeds, 57 Multipliers, Lagrange, 294 MUSCL scheme, 188 Mushy regions, 289 NACA0012 aerofoil, 84, 148, 202, 203, 204, 207 Natural boundary condition, 243, 252 Natural condition, 94 Natural convection, 144, 155, 158, 286 Natural convection in cavities, 156 Navier±Stokes equations, 8, 9, 10, 12, 26, 146, 150, 170±172, 180, 197, 210, 212, 219 275, 291 Reynolds Averaged, 162 Navigation, 218 Nearly implicit form, 42, 76 Nearly incompressible ¯ows, 10 Negative di€usion, 22 Negative waves, 235 Nevada desert, 193 Newton±Raphson iterations, 130 No-slip (boundary condition), 82 Nodal coordinates, 275 Nodal pressure switches, 286 Nodal quantities, 283 Node: boundary, 276, 280, 299 inside, 299 Noise, 250 Non-conservative equations, 9 Non-conservative form, 291 Non-linear solution, iterative, 96 Non-linear viscosity, 118 Non-linear waves, 48, 268 (See also Stokes waves, Korteweg±de Vries equation) Non-newtonian ¯ows, 2, 6, 91, 118 Non-re¯ecting boundary conditions, 253 Non-self-adjoint equations, 1, 15
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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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268 Waves wave elevations in shallo
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270 Waves integrals. Preliminary re
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272 Waves 39. R.J. Astley. FE mode
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 and 336: 322 Subject index Flows: buoyancy d
Page 337: 324 Subject index Incompressible St
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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