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

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procedure is somewhat involved and has been used with success in many trial problems as shown by Zienkiewicz and Wu. 80 We shall not describe the method in detail here but essentially structured meshes again composed of triangles or at least quadrilaterals divided into two triangles were used near the boundary and in the shock regions. The subdivision and accuracy obtained was excellent. In the second method we could imagine that normals are created on the boundaries, and a boundary layer thickness is predicted using some form of boundary layer analytical computation. 30ÿ33 Within this layer structured meshes are adopted using a geometrical progression of thickness. The structured boundary layer meshing can of course be terminated where its need is less apparent and unstructured meshes continued outside. In this procedure we shall use the simple direct re®nement of the type discussed in the previous section. Figure 6.25 illustrates supersonic ¯ow around an NACA0012 aerofoil using the automatic generation of structured and unstructured domains taken from reference 80. The second method is illustrated in Fig. 6.26 on a two-component aerofoil. 6.11 Three-dimensional viscous problems (a) Three-dimensional viscous problems 207 Fig. 6.27 Hypersonic viscous ¯ow at Mach 8.15 over a double ellipsoid. 31 (a) Initial surface mesh total nodes: 25 990 and elements: 139 808, The same procedures which we have described in the previous section can of course be used in three dimensions. Quite realistic high Reynolds number boundary layers were
208 Compressible high-speed gas ¯ow (b) (c) (d) Fig. 6.27 (Continued) (b) adapted mesh total nodes: 79 023 and elements: 441 760, (c) pressure contours, (d) Mach contours. so modelled. Figure 6.27 shows the viscous ¯ow at a very high Reynolds number around a forebody of a double ellipsoid form. 31 In this example a structured boundary layer is assumed a priori. The second example concerns a more sophisticated use of a structured subgrid procedure using local normals executed for a turbulent ¯ow around an ONERA M6 wing attached to an aircraft body (Fig. 6.28). 34
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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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Page 169 and 170: 156 Free surfaces, buoyancy and tur
Page 183 and 184: 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 243 and 244: 230 Shallow-water problems FL: 578
Page 245 and 246: 232 Shallow-water problems B Fig. 7
Page 247 and 248: 234 Shallow-water problems Time = 0
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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
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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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