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46. P. Nithiarasu, K.N. Seetharamu and T. Sundararajan. Natural convective heat transfer in an enclosure ®lled with ¯uid saturated variable porosity medium. Int. J. Heat Mass Transfer, 40, 3955±67, 1997. 47. S. Ergun. Fluid ¯ow through packed columns. Chem. Eng. Prog., 48, 89±94, 1952. 48. G. Lauriat and V. Prasad. Non-Darcian e€ects on natural convection in a vertical porous enclosure. Int. J. Heat Mass Transfer, 32, 2135±48, 1989. 49. P. Nithiarasu, K.N. Seetharamu and T. Sundararajan. Double-di€usive natural convection in an enclosure ®lled with ¯uid saturated porous medium ± a generalised non-Darcy approach. Numerical Heat Transfer, Part A, Applications, 30, 413±26, 1996. 50. P. Nithiarasu, K.N. Seetharamu and T. Sundararajan. E€ects of porosity on natural convective heat transfer in a ¯uid saturated porous medium. Int. J. Heat Fluid Flow, 19, 56±8, 1998. 51. P. Nithiarasu and K. Ravindran. A new semi-implicit time stepping procedure for buoyancy driven ¯ow in a ¯uid saturated porous medium. Comp. Meth. Appl. Mech. Eng., 165, 147±54, 1998. 52. P. Nithiarasu, K.N. Seetharamu and T. Sundararajan. Numerical prediction of buoyancy driven ¯ow in a ¯uid saturated non-Darcian porous medium. Int. J. Heat Mass Transfer, 42, 1205±15, 1999. 53. P. Nithiarasu. Finite element modelling of migration of a third component leakage from a heat source buried into a ¯uid saturated porous medium. Math. Comp. Modelling, 29, 27±39, 1999. 54. P. Nithiarasu, K.S. Sujatha, K.N. Seetharamu and T. Sundararajan. Buoyancy driven ¯ow in a non-Darcian ¯uid saturated porous enclosure subjected to uniform heat ¯ux ± a numerical study. Comm. Num. Meth. Eng., 15, 765±76, 1999. 55. P. Nithiarasu, N. Massarotti and O.C. Zienkiewicz. Finite element computations of porous media ¯ows, (to be published). 56. M. Wolfstein. Some solutions of plane turbulent impinging jets. ASME J. Basic Eng., 92, 915±22, 1970. 57. B.E. Launder and D.B. Spalding. Mathematical Models of Turbulence. Academic Press, N.Y., 1972. 58. P. Hood and C. Taylor. Navier±Stokes equations using mixed interpolation, J.T. Oden et al. (Ed.). Finite Element Method in Flow Problems, UAHPress, Huntsville, AL, pp. 121±32, 1974. 59. K. Morgan, T.G. Hughes and C. Taylor. An investigation of a mixing length and twoequation turbulence model utilising the ®nite element method. App. Math. Modelling, 1, 395±9, 1977. 60. C. Taylor, T.G. Hughes and K. Morgan. Finite element solution of one equation models of turbulent ¯ow. J. Comp. Phys., 29, 163±72, 1978. 61. A.J. Baker. Finite element analysis of turbulent ¯ows. Proc. Int. Conf. Num. Meth. in Laminar and Turbulent Flows, Swansea, 1978. 62. C.K.G. Lam and K. Bermhorst. A modi®ed form of -" model for predicting wall turbulence. J. Fluids Eng., 103, 456±60, 1981. 63. M. Srinivas, M.S. Ravisanker, K.N. Seetharamu and P.A. Aswathanarayana. Finite element analysis of internal ¯ows with heat transfer. Sadhana ± Academy Proc. Eng., 19, 785±816, 1994. 64. O.C. Zienkiewicz, B.V.K.S. Sai, K. Morgan and R. Codina. Split characteristic based semiimplicit algorithm for laminar/turbulent incompressible ¯ows. Int. J. Num. Meth. Fluids, 23, 1±23, 1996. 65. J. JimeÂ nez, A. Wray, P. Sa€man and R. Rogallo. The structure of intense vorticity in isotropic turbulence. J. Fluid Mech., 255, 65±90, 1993. 66. P. Moin and K. Mahesh. Direct numerical simulation: A tool in turbulence research. Ann. Rev. Fluid Mech., 30, 539±78, 1998. References 167
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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)
Page 129 and 130: 116 Incompressible laminar ¯ow (b)
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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
Page 179: 166 Free surfaces, buoyancy and tur
Page 183 and 184: 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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