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

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Residuals, 287 interpolation of, 301 Resistance, frictional, 226 Resonant cavity, 243 Response: periodic, 226 wave, 250 Restoration of connectivity, 181 Restriction: BabusÆ ka±Brezzi (BB), 66, 78, 80 Retardation, 245 Reverser, hemispheric th<strong>ru</strong>st, 96 Reynolds averaged Navier±Stokes equations, 162 Reynolds averaging, 10 Reynolds Number, 66, 97, 98, 115, 149, 156, 163, 164, 276 high, 207 very high, 208 Reynolds shear stress, 143, 162 Reynolds viscosity, 10 Rheology, numerical, 132 RHS (Right Hand Side) vector, 284, 253, 298 Riemann analysis, 172, 233 Riemann invariants, 58 Riemann shock tube, 177 Rigid±plastic, 120 Rip currents, 235 River Severn, 229 Rivers, 218 RMS departure error, 106 Rocket, 196, 197 Rubbers, synthetic, 132 Rudder, 150, 153 Runge±Kutta scheme, 55, 56 Sailing boat, 150, 153 Sailing speed, 150 Salinity, 238, 239 Scalar convection±di€usion equation, 92 Scalar equations, transient, 34 Scalar, steady-state, 26 Scattering problem, 246, 250 Scheme: CBS, 14 explicit, 43 MUSCL, 188 Runge±Kutta, 56 <strong>Taylor</strong>±Galerkin, 85 two-step, 84 Seaward limit, 233 Secant viscosity, 118 Second derivative based methods, 175 Second derivative of pressure, 280, 283 Second derivative shock capture, 186 Second derivatives, 107 Second re®nement, 205 Second-order wave elevation, 268±271 Sediments, transport of, 218, 237 Self-adjoint equation, 1, 14, 96 Self-adjointness, 31 Semi-explicit algorithms, 227 Semi-explicit forms, 275 Semi-implicit form, 76, 224, 284 Semi-inverse coupling, 303 Separation, 245, 303 boundary layer, 211 ¯ow, 171, 245 Series solutions, 253 exterior, 255 linking to, 256 Series, in®nite harbour, 235 Severn barrage, 226 Severn bore, 232, 233 Severn Estuary, 226, 229, 230, 231, 232, 236 Severn tsunami, 234 Severn, River, 229 Shallow water ¯ow, 3, 50, 219 Shallow-water equations, 223 Shallow-water problem, 218, 222, 274 Shallow-water theory, 265, 266 Shallow-water transport, 237 Shape function: convected, 37 linear, 16 Shape parameter: velocity pro®le, 304 Sharp discontinuity, 181 Shear modulus, 5, 115 Shear stress: Reynolds, 162 Shear stress coe cient, 304 Shear stresses, surface, 221 Shear viscosity, dynamic, 5 Shear, bottom, 221 Shedding: eddy, 3 vortex, 114 Sheet forming, 122 Shelving beach, 224 Ship, 3, 144 Ship hydrodynamics, 145, 146 Ship motion, 145 Shoal: parabolic, 257 Shoaling of a wave, 225 Shock, 9, 200, 235 stationary, 182 Shock capture, 52, 174, 176, 180, 186, 275, 276, 280, 286 Shock development, 3 Shock ®tting, 174 Shock front, 196 Subject index 329
330 Subject index Shock interaction, 201 Shock like behaviour, 28 Shock propagation, 50 Shock regions, 197 Shock tube, 224 Riemann, 177 Shock wave re¯ection, 182 Shock wave, 236 bow, 187 Shocks, 48, 108, 206, 218, 226, 286, 292 localizing, 181 Short-wave problem, 245 Shuttle, 196, 197 Side boundaries, 235 Side repeated, 235 Simulation, direct numerical, 161 Single-step algorithm, 80, 84 Situations, steady-state, 15 Size: average particle, 159 smallest element, 181 Skin friction, 202, 304 SLIP, 82 Slip boundary, 123, 235 Slip conditions, 83 Slow ¯ows, 113 Slow speeds, very, 2 Sluice gate, 144 Small waves, 147 Smallest element size, 181 Smearing, 29, 50, 179 Smoothing, 176 Solid wall boundary, 172, 173 Solidi®cation, 157, 274 Solids, incompressible elastic, 66 Solitary wave, 224, 268 Solution: banded, 276 boundary, 146 boundary layer, 305 CBS, 200 coarse mesh, 300 Euler, 192 exterior, 253 exterior series, 255 implicit, 54 inviscid Euler, 209 iterative non-linear, 96 oscillation-free, 100 Navier±Stokes, 171 pure Euler, 209 quasi-implicit, 98 quasi-implicit, 103 quasi-implicit, 104 series, 253 transient, 15 Solution methods, direct, 169 Solution of simultaneous equations, 286 Solution procedure, 70 Solution procedures, iterative, 147 Solver, banded, 286 Sommerfeld (radiation condition), 250 Sound: speed of, 3, 64, 172±178 Source, 73 Source term, 237 variable, 22 heat, 8 Spatial discretization, 70 Special ®nite elements, 249 Speci®c energy, 92, 94 Speci®c heat, 64, 92, 121, 156, 170 constant volume, 170 Speed: sailing, 150 Speed of sound, 3, 64, 172, 175, 178 Speeds: multiple wave, 57 propagation, 172 transonic, 48 very slow, 2 Sphere di€raction, elastic, 262 Spherical polar coordinates, 261 Spheroidal coordinates: oblate, 261 prolate, 261 Spiral mode, 264 Split: CBS (Characteristic Based), 59, 83 Chorin, 67 operator, 36 Split A, 68, 70, 78, 79, 80, 84 Split B, 68, 69, 75, 78, 79, 83 Sponge layer, 254 Spring-back, 131 Spurious oscillation, 50 Square cavity, closed, 156 SSC, THRUST, 191 St Michel, Mont, 236 Stability, 37, 38, 81, 250 Stability condition, 42 Stability limit, 42, 54, 76 Stability, conditional, 38 Stabilization, 39, 66, 70, 78, 80, 81, 113, 280, 284 Stable, unconditionally, 54 Stagnation point, 204 Stagnation stream, 302 State relationship, 10 State, equation of, 7, 67 Statement: weak, 294 weighted residual, 264
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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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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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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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Page 305 and 306: 292 Appendix A Again substituting t
Page 307 and 308: 294 Appendix B As usual the domain
Page 309 and 310: 296 Appendix B 5. While the piecewi
Page 311 and 312: Appendix C Edge-based ®nite elemen
Page 313 and 314: Appendix D Multigrid methods It is
Page 315 and 316: Appendix E Boundary layer±inviscid
Page 317 and 318: 304 Appendix E In Fig. E.2, Cp is t
Page 320 and 321: Author index Page numbers in bold r
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Page 324 and 325: Nakos, D.E. 146, 165 Narayana, P.A.
Page 326: Wu, J. 67, 90; 102, 108, 112, 137;
Page 329 and 330: 316 Subject index Blurring of the s
Page 331 and 332: 318 Subject index Convected coordin
Page 333 and 334: 320 Subject index Elements ± cont.
Page 335 and 336: 322 Subject index Flows: buoyancy d
Page 337 and 338: 324 Subject index Incompressible St
Page 339 and 340: 326 Subject index Metals: hot, 120
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Page 345 and 346: 332 Subject index Theorem ± cont.
Page 347: 334 Subject index Wave ± cont. ste
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