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

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a posteriori error indicators, 244 A, split see Split, A Absolute temperature, 7, 92, 154 Absorption of acoustic waves, 242 Acceleration: convective, 1, 65 Accelerations, Coriolis, 221 Accuracy of in®nite elements, 264 Acoustics, 3, 11, 219, 242, 243, 245, 250, 262, 264 exterior, 261 Adaptive development, 180 Adaptive mesh, 205 generation, 113 re®nement, 102 Adaptive procedure, 206, 275 Adaptive re®nement, 132, 180, 200, 206 Adaptive remeshing, 126, 195 Adaptivity, 189 Advancing boundary normals, 206 Advancing front technique, 148 Advective term, 25 Aerofoil, 95, 202, 302 NACA0012, 84, 148, 202±207 two-component, 206 Aeronautics, 170 Aircraft, 189, 192, 209, 212, 246 ALE (Arbitrary Lagrangian±Eulerian) method, 128 Algorithm: (See also methods, procedures, process) CBS (Characteristic Based Split), 84, 85, 92, 93, 98, 113, 132, 147, 156, 159, 162, 173, 188, 198, 202, 224, 237, 274, 278, 284 characteristic Galerkin, 43 DtN, 253 explicit, 100 semi-explicit, 227 single-step, 84 Alloys, solidi®cation of, 157 Aluminium, 120 Subject index Angular frequency, 242, 243 Anisotropic di€usion, 28 Anisotropic mesh generation, 109 Anisotropic shock capturing, 176, 186, 280 Anisotropic viscosity, 174 Arti®cial compressibility, 67, 99 Arti®cial di€usion, 22, 50, 175, 224 Lapidus-type, 179 Arti®cial dissipation, 174 Arti®cial island problem, 259 Arti®cial o€shore harbour, 258 Arti®cial viscosities, 174, 280 Atmospheric pressure, 220 Automatic generation of meshes, 182 Auxiliary variable, 69 Average ¯uxes, 294 Average particle size, 159 Average pressure, 175 Averaged ¯ow equations, 162 Averaged heat capacity, 159 Avonmouth, 229 Axisymmetric jet, 96 B split, see Split, B BabusÆ ka±Brezzi (BB) restrictions, 66, 78, 80, 117 Backward facing step, 100, 105, 113, 164 Balance of energy, 8 Balance of momentum, 6, 242 Balancing di€usion, 20, 22, 27 streamline, 28 Banded solution, 276, 286 Basin, 243 Bathygraphy, 227 Beach, shelving, 224 Bed friction, 226, 235, 245 Beer cans, 130 Berkho€ wave theory, 265, 266 Bernoulli's equation, 94, 147, 265, 266 Bingham ¯uid, 118, 119 Blunt body, 184
316 Subject index Blurring of the shock, 181 Boat: sailing, 150, 153 Body di€racting, 251 Body forces, 8, 65, 73, 92, 94, 96 Boeing 747, 189 Bore, 224, 227 Severn, 232, 233 tidal, 229 Bottom drag stresses, 222 Bottom shear, 221 Bottom-heating cavities, 156 Boundaries: changing, 124 exterior, 173 external, 172 ®ctitious, 81 in®nite, 173 side, 235 supersonic out¯ow, 173 Boundary: external, 227 ®ctitious, 172 in®nite, 261 outer, 251 slip, 123, 235 solid wall, 172, 173 supersonic in¯ow, 172 Boundary at in®nity, 251 Boundary condition, 94 free, 233 natural, 243, 252 Boundary conditions, 81, 82, 279, 284 Dirichlet, 293, 294 Euler, 305 inlet, 45 local non-re¯ecting, 253 non-re¯ecting, 253 prescribed traction, 83 radiation, 44 Boundary dampers, 253 Boundary forces, 91 Boundary integrals, 252, 256, 262 exterior, 255 linking to, 255 Boundary layer, 3, 10, 16, 108, 110, 171, 180, 192, 197, 198, 200, 202, 206, 209, 210, 222 interaction, 201 separation, 211 solution, 305 theory, 212 thickness, 207, 304 ±inviscid ¯ow coupling, 302 Boundary node, 276, 280, 299 Boundary normals, advancing, 206 Boundary operators, 250 Boundary solution, 146 Boundary tractions, 83 Boundary velocities, prescribed, 120 Boundary-exit conditions, 100 Boussinesq model, 162 Bow shock wave, 187 Breakwater: ¯oating, 265±267 Breakwaters, 250 permeable, 245 Bristol Channel, 226±231, 236 Bulk modulus, 5, 11, 64, 91, 92, 242 Buoyancy, 143 Buoyancy driven convection, 161 Buoyancy driven ¯ows, 153, 156 Buoyancy force, 91 Burger's equation, 50, 52 Burnett elements, 261, 262 Car: motor, 192 supersonic, 191 Car bodies, 130 Cartesian coordinates, 275 Cauchy±Poisson free surface condition, 265, 266 Cavities, bottom-heating, 156 Cavity problem, driven, 115 Cavity, 99 closed square, 97, 156 lid-driven, 100, 101, 103, 104, 111 resonant, 243 CBS (Characteristic Based Split) algorithm, 14, 64, 67, 83±85, 92, 93, 98, 113, 132, 147, 156, 159, 162, 173, 188, 198, 200, 202, 224, 237, 274, 274, 275, 276, 278, 279, 284, 289 CBS algorithm incompressible ¯ows, 97 CBS algorithm, computer implementation, 274 Central ®nite di€erence form, 18 Changing boundaries, 124 Channel: Bristol, 226±236 rectangular, 228, 235 symmetric, 236 Characteristic directions, 33 Characteristic Galerkin algorithm, 34, 43 Characteristic variable, 175 Characteristic-based methods, 35 Characteristic-based procedures, upwinding, 59 Characteristic-based split, 59 Characteristic-based split algorithm, see CBS Characteristic±Galerkin, 36, 38, 48, 67±69, 74, 146, 176, 237, 246 Characteristics, 34, 35, 73 Charge density, 243 Chemical concentrations, 75 Chemical reaction, 8
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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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Page 281 and 282: 268 Waves wave elevations in shallo
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
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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
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Page 324 and 325: Nakos, D.E. 146, 165 Narayana, P.A.
Page 326: Wu, J. 67, 90; 102, 108, 112, 137;
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 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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