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

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6.6.1 Riemann shocktube ± a transient problem in one dimension 1 This is treated as a one-dimensional problem. Here an initial pressure di€erence between two sections of the tube is maintained by a diaphragm which is destroyed at t ˆ 0. Figure 6.2 shows the pressure, velocity and energy contours at the seventieth time increment, and the e€ect of including consistent and lumped mass matrices is illustrated. The problem has an analytical, exact, solution presented by Sod 57 and the numerical solution is from reference 1. 6.6.2 Isothermal ¯ow through a nozzle in one dimension Here a variant of the Euler equation is used in which isothermal conditions are assumed and in which the density is replaced by a where a is the cross-sectional ρ 1.000 0.425 0 t = 0 u Lumped mass e 2.5 2.0 Some preliminary examples for the Euler equation 177 t = 18.5 Consistent mass Fig. 6.2 The Riemann shocktube problem. 1;57 The total length is divided into 100 elements. Pro®le illustrated corresponds to 70 time steps ( t ˆ 0:25). Lapidus constant C Lap ˆ 1:0.
178 Compressible high-speed gas ¯ow area 1 assumed to vary as 58 …x ÿ 2:5†2 a ˆ 1:0 ‡ 12:5 for 0 4 x 4 5 …6:20† The speed of sound is constant as the ¯ow is isothermal and various conditions at in¯ow and out¯ow limits were imposed as shown in Fig. 6.3. In all problems 2.0 1.5 ρ 1.0 0.5 0 0 1.0 2.0 x 3.0 4.0 (a) Subsonic inflow and outflow 2.0 1.5 ρ 1.0 0.5 0 0 1.0 2.0 x 3.0 4.0 (b) Supersonic inflow and outflow 2.0 1.5 ρ 1.0 0.5 0 0 1.0 2.0 x 3.0 4.0 2.0 1.5 u 1.0 0.5 0 0 1.0 2.0 x 3.0 4.0 2.0 1.5 u 1.0 0.5 (c) Supersonic inflow–subbsonic outflow with shock Exact C L = 2.0 C L = 1.0 0 0 1.0 2.0 x 3.0 4.0 2.0 1.5 u 1.0 0.5 0 0 1.0 2.0 x 3.0 4.0 u' 0.75 a/2 0.5 u 0.0 5.0 2 C1 C1 Fig. 6.3 Isothermal ¯ow through a nozzle. 1 Forty elements of equal size used.
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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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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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Page 231 and 232: 7 Shallow-water problems 7.1 Introd
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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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