Che zy, 221, 245 Chorin split, 67 Circular cylinder, 269 Civil aircraft, 189 Closed cavity, 97, 156 Closed domains, waves in, 243 Closure models, ®rst-order, 162 Cnoidal waves, 268 Coastal engineering, 223 Coastal estuaries, 218 Coastlines, 250 Coe cient: arti®cial di€usion, 175 Che zy, 221 di€usion, 14, 237 di€usion conduction, 293 entrainment, 304 Manning friction, 229 shear stress, 304 skin friction, 304 viscosity, 221 Coe cient of pressure, 304 Coe cient of thermal expansion, 154 Collocation, subdomain, 2 Complex conjugate weighting, 246, 260, 263 Compressibility, 2, 3, 64 arti®cial, 67, 99 elastic, 132 Compressible ¯ow, 10, 48, 50, 66, 73, 91, 108, 170, 173, 174, 218, 224, 275 Compressible gases, 57, 169 Compressible high-speed ¯ows, 57, 280 Compressible viscous ¯ow problems, 274 Compressible wave celerity, 172 Computer implementation of the CBS algorithm, 274 Concentration, 289 Concentrations, chemical, 75 Condition: boundary, 94 free boundary, 233 free surface, 96, 265, 266 kinematic, 265, 266 Kutta±Joukoski, 150 natural, 94 natural boundary, 243, 252 radiation, 250, 269 Rankine±Hugoniot, 50 stability, 42 Conditional stability, 38 Conditioning system matrix, 250 Conditions: boundary, 81, 82, 279, 284 boundary-exit, 100 Dirichlet boundary, 293, 294 equilibrium, 304 Subject index 317 Euler boundary, 305 incompressibility, 66 inlet boundary, 45 isothermal, 177 non-re¯ecting boundary, 253 radiation, 251 radiation boundary, 44 ramp, 97 slip, 83 steady-state, 79 Conduction coe cient, di€usion, 293 Conduction, heat, 8, 275 Conductive heat ¯ux, 8 Conductivity ratio, 66, 276 thermal, 161 Conductivity: isotropic thermal, 8 thermal, 65, 66, 156, 159, 161 Conjugate gradient procedures, 77 Conjugate gradient, diagonal preconditioned, 286 Conjugate weighting, complex, 260, 263 Conjugated in®nite elements, 264 Connectivity, 275 restoration of, 181 Conservation: complete ¯ux, 293 energy, 7, 65 energy, 124 mass, 6, 219, 242 momentum, 6, 65, 219 Conservation equation, energy, 3 Conservation form, 8, 171, 246, 286 Conservation laws, 13 Conservation of energy, 66, 92, 291 Conservation of mass, 64, 66, 91, 291 Conservation of momentum, 66, 92, 291 Conservative variables, 298 Consistent mass matrices, 43, 175, 177, 284, 298 Constant: Che zy, 245 dielectric, 243 Lapidus, 180 universal gas, 7, 65, 154, 170 Constant entropy, 64 Constant pressure, 170 Constant volume speci®c heats, 170 Constitutive relation for ¯uids, 5 Constraints, 294 incompressible, 1, 2 Continuity, 19, 99, 159, 162, 304 Continuity, depth-averaged, 221 Continuum problems, 2 Contours: density, 86, 203 Mach, 208 pressure, 208, 210
318 Subject index Convected coordinates, 124 Convected shape function, 37 Convection, 4, 8 buoyancy driven, 161 forced, 144, 286 heat, 238 mixed, 286 natural, 155, 158, 286 naturally occurring, 144 pure, 29, 45 Rayleigh±Bernard, 156 Convection dominated problems, 13 Convection equation, pure, 146 Convection velocity, 293 Convection±di€usion equation, 4, 13, 25, 26, 44, 47, 72, 92, 293 Convective acceleration, 1, 65 Convective di€usion, 34, 36 Convective forces, 55 Convective motion, 157 Convective term, 14, 96 Convergence, 97, 188, 287±289, 300 Coordinates: cartesian, 275 convected, 124 ellipsoidal, 261, 262 nodal, 275 oblate spheroidal, 261 prolate spheroidal, 261 spherical polar, 261 Coriolis accelerations, 221 Coriolis forces, 229 Coriolis parameter, 221 Corners, re-entrant, 245 Correction: mass matrix, 284 momentum, 279 Coupling: energy, 279 semi-inverse, 303 thermal, 11, 125 viscous-inviscid, 210, 211 Courant Number, 42, 97 Criteria, convergence, 289 Critical ¯ows, super, 235 Critical stable upwind parameter, 20 Critical time step, 224 Cross-waves, 235 Cross-wind di€usion, 29 Current, 243 Currents: density-induced, 11 longshore, 235 rip, 235 tidal, 238 Curvature based re®nement, 102 Curvature of the streamlines, 110 Curvatures, 107 maximum principle, 108 minimum, 109 Cylinder: circular, 269 full, 185 Dam break, 224, 226 Damper: cylindrical, 253 Damper-related approaches, 254 Dampers: boundary, 253 cylindrical, 253 higher-order, 254 plan, 253 transient, 265 Damping term, 252 Damping, optimal, 78 Darcy Number, 160, 161, 276 DARPA submarine model, 149, 152 Dassault, 189 Data input, 275 Data, mesh, 275 Decay function procedures, 259 Decomposition, Riemann, 233 Decoupled equations, 58 Deep drawing, 122, 129 Deep water, 268 Delaunay triangulation, 109 Delta: Kronecker, 5, 65 Density, 3, 7, 91, 92, 154, 170, 304 charge, 243 ¯uid, 6 Density contours, 86, 203 Density variation, 278 Density-induced currents, 11 Density±pressure equation, 73 Density/pressure ®elds, 284 Depth: total, 220 water, 242, 243 Depth-averaged continuity, 221 Depth-averaged governing equations, 220 Depth-averaged transport equations, 237 Derivatives, second, 107 Desert, Nevada, 193 Design, aircraft, 192 Deviatoric strain, 5, 71, 72 Deviatoric stress, 1, 5, 65, 71, 72, 92 DGM, 295 Diagonal matrix, 58, 72 Diagonal preconditioned conjugate gradient, 286
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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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4 Introduction and the equations of
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6 Introduction and the equations of
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3 A general algorithm for compressi
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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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110 Incompressible laminar ¯ow 4.5
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112 Incompressible laminar ¯ow 4.5
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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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146 Free surfaces, buoyancy and tur
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148 Free surfaces, buoyancy and tur
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150 Free surfaces, buoyancy and tur
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152 Free surfaces, buoyancy and tur
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154 Free surfaces, buoyancy and tur
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156 Free surfaces, buoyancy and tur
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158 Free surfaces, buoyancy and tur
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160 Free surfaces, buoyancy and tur
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162 Free surfaces, buoyancy and tur
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164 Free surfaces, buoyancy and tur
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166 Free surfaces, buoyancy and tur
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168 Free surfaces, buoyancy and tur
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170 Compressible high-speed gas ¯o
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172 Compressible high-speed gas ¯o
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174 Compressible high-speed gas ¯o
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176 Compressible high-speed gas ¯o
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188 Compressible high-speed gas ¯o
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190 Compressible high-speed gas ¯o
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192 Compressible high-speed gas ¯o
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200 Compressible high-speed gas ¯o
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204 Compressible high-speed gas ¯o
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206 Compressible high-speed gas ¯o
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208 Compressible high-speed gas ¯o
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210 Compressible high-speed gas ¯o
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212 Compressible high-speed gas ¯o
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214 Compressible high-speed gas ¯o
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216 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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- Page 305 and 306: 292 Appendix A Again substituting t
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- 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: 316 Subject index Blurring of the s
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