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

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well known that the Euler solution is perfectly capable of simulating all shocks very adequately and indeed results in very well de®ned pressure distributions over the bodies whether it is over an aircraft or a car. The object of the analysis was indeed that of determining such pressure distributions and the lift caused by these pressures. It was essential that the car should remain on the ground, indeed this is one of the conditions of the ground speed record and any design which would result in substantial lift overcoming the gravity on the car would be disastrous for obvious reasons. The complete design of the supersonic car was thus made with several alternative geometries until the computer results were satisfactory. Here it is interesting however to have some experimental data and the preliminary con®guration was tested by a rocket driven sled. This was available for testing rocket projectiles at Pendine Sands, South Wales, UK. Here a 1:25 scale model of the car was attached to such a rocket and 13 supersonic and transonic runs were undertaken. In Fig. 6.13(a), we show a photograph 27 of the car concerned after winning the speed record in the Nevada desert. In Fig. 6.13(b) a surface mesh is presented from which the full three-dimensional mesh at the surrounding atmosphere was generated (surface mesh, nodes: 39 528, elements: 79 060; volume mesh, nodes: 134 272, elements: 887 634). We do not show the complete mesh as of course in a three-dimensional problem this is counterproductive. In Fig. 6.14, pressure contours 27 on the surface of the car body are given and somewhat similar contours are shown on the covers of this book. In Fig. 6.15, a detailed comparison of CFD results 27 with experiments is shown. The results of this analysis show a remarkable correlation with experiments. The data points which do not appear close to the straight line are the result of the sampling point being close to, but the wrong side of, a shock wave. If conventional correlation techniques for inviscid ¯ow (viscous correction) are applied, these data points also lie on the straight line. In total, nine pressure points were used situated on the upper and Key M = 0.71 M = 1.08 M = 0.96 M = 1.05 CFD results 6 4 2 –6 –4 –2 2 4 6 8 P.S.L Pendine tests –2 Pendine test results –4 –6 Three-dimensional inviscid examples in steady state 193 Computer results Fig. 6.15 Supersonic car, THRUST SSC 27 comparison of ®nite element and experimental results.
194 Compressible high-speed gas ¯ow lower surfaces of the car. The plot shows the comparison of pressures at speci®c positions on the car for Mach numbers of 0.71, 0.96, 1.05 and 1.08. 6.8.3 Other examples There are many other three-dimensional examples which could at this stage be quoted but we only show here a three-dimensional analysis of an engine intake 16 at Mach 2. This is given in Fig. 6.16. (a) Mesh on analysis surface (b) Mesh on analysis surface (c) Pressure contours Fig. 6.16 Three-dimensional analysis of an engine intake 16 at Mach 2 (14 000 elements).
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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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Page 157 and 158: 144 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
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Page 255 and 256: 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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