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

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and Lumped C = 0.5, 1/T Lumped C = 0.1, 1/T C = 0.5, 2/T C = 0.1, 2/T Consistent Consistent C = 0.5, 3/T C = 0.1, 3/T (a) Courant number = 0.5 (b) Courant number = 0.1 Characteristic-based methods 45 Lumped/consistent M Courant number = 0.5 Courant number = 0.1 Fig. 2.16 Characteristic±Galerkin method in the solution of a one-dimensional wave progression. Effect of using a lumped mass matrix and of consistent iteration. ÿk @ @n ˆ q on ÿ q …2:105b† (where ÿ ˆ ÿu [ ÿq) to be imposed, providing the equation is of second order and di€usion is present. In the case of pure convection this is no longer the case as the di€erential equation is of ®rst order. Indeed this was responsible for the di culty of obtaining a solution in the example of Fig. 2.2 when Pe !1and an exit boundary condition of the type given by Eq. (2.105a) was imposed. In this one-dimensional case for pure convection only the inlet boundary condition can be given; at the exit no boundary condition needs to be prescribed if U, the wave velocity, is positive. For multidimensional problems of pure convection the same wave speci®cation depends on the value of the normal component of U. Thus if Uini > 0 …2:106† where n i is the normal direction vector, the wave is leaving the problem and then no boundary condition is speci®ed. If the problem has some di€usion, the same
46 Convection dominated problems speci®cation of `no boundary condition' is equivalent to putting ÿk @ @n ˆ 0 …2:107† at the exit boundary. In Fig. 2.17 we illustrate, following the work of Peraire, 65 how cleanly the same wave as that speci®ed in the problem of Fig. 2.15 leaves the domain in the uniform velocity ®eld 61;65 when the correct boundary condition is imposed. Initial configuration Fig. 2.17 A gaussian distribution advected in a constant velocity ®eld. Boundary condition causes no re¯ection.
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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
Page 7 and 8: 3.7 The performance of two- and sin
Page 9 and 10: ...................................
Page 11 and 12: Volume 2: Solid and structural mech
Page 13 and 14: xiv Preface to Volume 3 this algori
Page 15 and 16: 2 Introduction and the equations of
Page 23 and 24: 10 Introduction and the equations o
Page 25 and 26: 12 Introduction and the equations o
Page 27 and 28: 14 Convection dominated problems We
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Page 33 and 34: 20 Convection dominated problems i.
Page 35 and 36: 22 Convection dominated problems 2
Page 37 and 38: 24 Convection dominated problems 2.
Page 39 and 40: 26 Convection dominated problems ar
Page 41 and 42: 28 Convection dominated problems Th
Page 43 and 44: 30 Convection dominated problems co
Page 45 and 46: 32 Convection dominated problems 2.
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Page 49 and 50: 36 Convection dominated problems an
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Page 55 and 56: 42 Convection dominated problems U
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Page 63 and 64: 50 Convection dominated problems To
Page 65 and 66: 52 Convection dominated problems C
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Page 75 and 76: 62 Convection dominated problems 47
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
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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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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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