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

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Stockpole Quay Western limit 1 Tenby Western limit 2 Port Isaac Worms Head Swansea Port Talbot Porthcawl Lynmouth Ilfracombe Fig. 7.6 Location map. Bristol Channel and Severn Estuary. Cardiff Barry Minehead Newport Beachley Hinkley Pt Watchet Avonmouth Clevedon the critical (explicit) time step (50 s), 4 times (200 s) and 8 times (400 s) the critical time step. A constant real friction coe cient (Manning) of 0.038 was adopted for all of the estuary. Coriolis forces were included. The analysis proved that the Coriolis e€ect was very important in terms of phase errors. Table 7.1 represents a comparison between observations and computations in terms of amplitudes and phases for seven di€erent points which are represented in the location map (Fig. 7.6), for the three di€erent time steps described above. The maximum error in amplitude only increases by 1.4% when the time step of 400 s is used with respect to the time step of 50 s, while the absolute error in phases (ÿ138) is two degrees more than the case of 50 s (ÿ118). These bounds show a remarkable accuracy for the semi-explicit model. In Fig. 7.8 the distribution of velocities at di€erent times of the tide is illustrated (explicit model). In the analysis presented we have omitted details of the River Severn upstream of the eastern limit (see Figs 7.6 and 7.9(a)), where a `bore' moving up the river can be observed. An approach to this phenomenon is made by a simpli®ed straight extension of the mesh used previously, preserving an approximate variation of the bottom and width until the point G (Gloucester) (77.5 km from Avonmouth), but obviously neglecting the dissipation and inertia e€ects of the bends. Measurement points are located at B and E, and the results (elevations) are presented in Fig. 7.9(d) for the points A, B, E in time, along with a steady river ¯ow. A typical shape for a tidal bore can be observed for the point E, with fast ¯ooding and a Eastern limit Weston-Super-Mare 0 50 km Examples of application 229
230 Shallow-water problems FL: 578 nodes, 1004 elements CL: 164 nodes, 251 elements 2 2 5 5 10 6 8 10 6 8 9 9 7 4 3 7 4 3 1 1 FR: 382 nodes, 664 elements CR: 111 nodes, 161 elements 5 Station Location 5 Hartland Point Tenby Ilfracombe Portlock Swansea Porthcawl Watchet Barry Weston-Super-Mare Avonmouth 1 2 3 4 5 6 7 8 9 10 10 6 8 10 6 8 9 9 7 4 3 7 4 3 Fig. 7.7 Finite element meshes. Bristol Channel and Severn Estuary.
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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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Page 231 and 232: 7 Shallow-water problems 7.1 Introd
Page 233 and 234: 220 Shallow-water problems reduced
Page 235 and 236: 222 Shallow-water problems Approxim
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Page 239 and 240: 226 Shallow-water problems h = 2 η
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Page 247 and 248: 234 Shallow-water problems Time = 0
Page 249 and 250: 236 Shallow-water problems Fig. 7.1
Page 251 and 252: 238 Shallow-water problems where no
Page 253 and 254: 240 Shallow-water problems 14. T.D.
Page 255 and 256: 8 Waves Peter Bettess 8.1 Introduct
Page 257 and 258: 244 Waves the familiar form where
Page 259 and 260: 246 Waves of 10 nodes or thereabout
Page 261 and 262: 248 Waves and the Astley wave envel
Page 263 and 264: 250 Waves agreement with the analyt
Page 265 and 266: 252 Waves Fig. 8.3 General wave dom
Page 267 and 268: 254 Waves Relative errors (%) 10 8
Page 269 and 270: 256 Waves (The indirect boundary in
Page 271 and 272: 258 Waves where m is the number of
Page 273 and 274: 260 Waves Fig. 17.6 of Volume 1. La
Page 275 and 276: 262 Waves to using such coordinate
Page 277 and 278: 264 Waves r/a 5 4 3 2 1 0 0 2 4 6 8
Page 279 and 280: 266 Waves 8.16 Three-dimensional ef
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
Page 289 and 290: 276 Computer implementation of the
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280 Computer implementation of the
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292 Appendix A Again substituting t
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294 Appendix B As usual the domain
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296 Appendix B 5. While the piecewi
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Appendix C Edge-based ®nite elemen
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Appendix D Multigrid methods It is
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Appendix E Boundary layer±inviscid
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304 Appendix E In Fig. E.2, Cp is t
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Author index Page numbers in bold r
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Gerdes, K. 259, 264, 265, 272 Ghia,
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Nakos, D.E. 146, 165 Narayana, P.A.
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Wu, J. 67, 90; 102, 108, 112, 137;
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316 Subject index Blurring of the s
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318 Subject index Convected coordin
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320 Subject index Elements ± cont.
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322 Subject index Flows: buoyancy d
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324 Subject index Incompressible St
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326 Subject index Metals: hot, 120
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328 Subject index Prescribed tracti
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330 Subject index Shock interaction
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332 Subject index Theorem ± cont.
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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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