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

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Streamlines Pressures (a) Stokes flow, viscosity 1, 9600 iterations (b) Re = 400, 4400 iterations (c) Re = 1000, 6100 iterations (d) Re = 5000, 48000 iterations Boundary-exit conditions 101 Fig. 4.6 Lid-driven cavity. Streamlines and pressure contours for different Reynolds numbers (semi-implicit form).
102 Incompressible laminar ¯ow p 1.5 1.0 0.5 0 –0.5 –1.0 '10x_uniform' '40x_unifom' 40x_non-uniform' –1.5 0 0.2 0.4 0.6 0.8 1.0 Fig. 4.7 Pressure distribution at mid-horizontal plane for Stokes ¯ow in a cavity for different meshes (semiimplicit form) and different boundary conditions. comparison, the results predicted by taking a longer domain downstream are also presented. As shown, the results predicted using the boundary conditions explained in Chapter 3, Sec. 3.6 are very accurate. 4.5 Adaptive mesh re®nement We have discussed the matter of adaptive re®nement in Chapters 14 and 15 of Volume 1 in some detail. In that volume we have generally strived to obtain the energy norm error to be equal within all elements. The same procedures concerning the energy norm error can be extended of course to viscous ¯ow especially when this is relatively slow and the problem is nearly elliptic. However, the energy norm has little signi®cance at high speeds and here we revert to other considerations which simply give an error indicator rather than an error estimator. Two procedures are available and will be used in this chapter as well as a later one dealing with compressible ¯ows. References 11±69 list some of the earlier and latest contributions to the ®eld of adaptive procedures in ¯uid mechanics. 4.5.1 Second gradient (curvature) based re®nement Here the meaning of error analysis is somewhat di€erent from that of the energy norm and we follow an approach where the error value is constant in each element. In what x 1
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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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Page 77 and 78: 3 A general algorithm for compressi
Page 79 and 80: 66 A general algorithm for compress
Page 105 and 106: 92 Incompressible laminar ¯ow Cons
Page 107 and 108: 94 Incompressible laminar ¯ow and,
Page 109 and 110: 96 Incompressible laminar ¯ow V/V
Page 111 and 112: 98 Incompressible laminar ¯ow The
Page 113: 100 Incompressible laminar ¯ow 1.5
Page 117 and 118: 104 Incompressible laminar ¯ow �
Page 119 and 120: 106 Incompressible laminar ¯ow x 2
Page 121 and 122: 108 Incompressible laminar ¯ow Thi
Page 123 and 124: 110 Incompressible laminar ¯ow 4.5
Page 125 and 126: 112 Incompressible laminar ¯ow 4.5
Page 127 and 128: 114 Incompressible laminar ¯ow (a)
Page 129 and 130: 116 Incompressible laminar ¯ow (b)
Page 131 and 132: 118 Incompressible laminar ¯ow wit
Page 133 and 134: 120 Incompressible laminar ¯ow The
Page 135 and 136: 122 Incompressible laminar ¯ow Fig
Page 137 and 138: 124 Incompressible laminar ¯ow and
Page 139 and 140: 126 Incompressible laminar ¯ow U U
Page 141 and 142: 128 Incompressible laminar ¯ow C L
Page 143 and 144: 130 Incompressible laminar ¯ow are
Page 145 and 146: 132 Incompressible laminar ¯ow sha
Page 147 and 148: 134 Incompressible laminar ¯ow Fig
Page 149 and 150: 136 Incompressible laminar ¯ow 28.
Page 151 and 152: 138 Incompressible laminar ¯ow 71.
Page 153 and 154: 140 Incompressible laminar ¯ow 114
Page 155 and 156: 142 Incompressible laminar ¯ow 153
Page 157 and 158: 144 Free surfaces, buoyancy and tur
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152 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
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9 Computer implementation of the CB
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276 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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