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| Donea J., Huerta A. — Finite Element Methods for Flow Problems |
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| Предметный указатель |
Reynolds transport theorem 12
Riemann problem 153
Riemann variables 164
Rotating cone problem 135
Rotating pulse problem, steady 250
Rotating pulse problem, transient 246
Runge — Kutta methods 215—216
Runge — Kutta methods, explicit 217
Runge — Kutta methods, implicit 217 220
Saddle point 273 277
Schur complement matrix 283
Second-order Taylor — Galerkin 98 (See also “Lax — Wendroff method”)
Semi-discrete method 92 94—95 222
Semi-Lagrangian method 80 87—89
SGS see “Sub-grid scale”
Shock 154
Shock tube problem 202
Shock-capturing techniques 177—180 182 184
Solenoidal velocity field 274—275
Solid boundary 165
Space-time formulation, Galerkin/Least-squares, convection-diffusion 241
Space-time formulation, Galerkin/Least-squares, Euler equations 175
Space-time formulation, Galerkin/Least-squares, pure convection 128
Space-time formulation, pure convection 126
Space-time formulation, time-discontinuous Galerkin 126
Space-time formulation, time-discontinuous least-squares 128
Spatial time derivative 7—8
Speed of sound 161
Spin tensor 267
Stability 98—99
Stability, convection-diffusion,  family methods 225
Stability, convection-diffusion, explicit Pads methods 229
Stability, explicit methods 225
Stability, pure convection 130
Stability, pure convection, classical time-stepping schemes 101
Stability, pure convection, Taylor — Galerkin method 110
Stability, pure convection, two-step Taylor — Galerkin method 115
Stability, Runge — Kutta 217
Stabilization matrix 233—234
Stabilization parameter 60
Stabilization parameter, convection-diffusion 64
Stabilization parameter, convection-diffusion-reaction 65
Stabilization parameter, Euler equations 174
Stabilization parameter, higher-order finite elements 65
Stabilization parameter, Navier — Stokes 297
Stabilization parameter, pure convection 129
Stabilization parameter, shock-capturing 185
Stabilization parameter, Stokes 288
Stabilization parameter, transient convection-diffusion-reaction 232
Stabilization techniques 59—60 168 231 233 241
Stabilization techniques, Galerkin/Least-squares 63 128 175 236.
Stabilization techniques, least-squares 120—122 128 237 254
Stabilization techniques, Streamline-upwind Petrov — Galerkin 60 172 236 296
Stabilization techniques, sub-grid scale 63 68 70 237
Stabilization techniques, variational multiscale 68
Stabilization, Euler equations 168 172 174—175
Stabilization, Navier — Stokes equations 296
Stabilization, nearly incompressible flows 187
Stabilization, steady, convection-diffusion 254
Stabilization, steady, convection-diffusion-reaction 59—60
Stabilization, Stokes equations 287
Stabilization, unsteady, convection-diffusion 254
Stabilization, unsteady, convection-diffusion-reaction 231 233 236—237 241
| Stabilization, unsteady, pure convection 120—122 128
Stable problem 98
Stokes flow equations 271
Stokes flow equations, Cauchy stress formulation, stress-strain vector form 277
Stokes flow equations, Cauchy stress formulation, strong form 275
Stokes flow equations, Cauchy stress formulation, weak form 275—276
Stokes flow equations, Galerkin 279
Stokes flow equations, matrix problem 281
Stokes flow equations, solvability condition 283
Stokes flow equations, stabilization 287
Stokes flow equations, velocity-pressure formulation, strong form 278
Stokes flow equations, velocity-pressure formulation, weak form 279
Stokes’ law 269
Strain rate tensor 267
Strain rate vector 277
Stream function 272
Streamline-upwind method 55
Streamline-upwind Petrov — Galerkin 60—62 233 236 257
Streamline-upwind Petrov — Galerkin, Euler equations 172—173
Streamline-upwind Petrov — Galerkin, Navier — Stokes 297
Streamline-upwind Petrov — Galerkin, space-time 175
Streamline-upwind test function 58 75
Stress-divergence form 270 275 278—279
Stress-strain vector form 277
Sub-grid scale 64 68—70 233 237
Sub-grid viscosity 68
Superconvergence 64
Supersonic boundaries 166
Supersonic flow 166
SUPG see “Streamline-upwind Petrov — Galerkin”
System of hyperbolic equations 86
Taylor least-squares method 122
Taylor — Galerkin methods 107
Taylor — Galerkin methods, one-step, fourth-order 113
Taylor — Galerkin methods, one-step, second-order 98 157
Taylor — Galerkin methods, one-step, third-order 108
Taylor — Galerkin methods, two-step, fourth-order 116
Taylor — Galerkin methods, two-step, second-order 158
Taylor — Galerkin methods, two-step, third-order 114
Taylor — Hood element 285—286
Time-discontinuous, Galerkin 126
Time-discontinuous, least-squares 128
Total Lagrangian formulation 5
Total time derivative 84 (See also “Material time derivative”)
Total variation diminishing 118—120 180—181
Transport equation 83
Triangulation 22
Unconditionally stable 225
Uniqueness 25—26 149—150 152—153 165 211 271 283—285 298 300
Updated Lagrangian formulation 5
Vanishing viscosity 153—154
Variational Principle 26
Velocity gradient 267
Viscosity matrix 281—282 290
Viscosity solution see “Entropy solution”
Von Neumann stability analysis 99
Vorticity tensor 267
wave number 100
Wave vector 100
Weak (or variational) form 24
Weak solution 85 149 153
Weighted residual formulation 24
Well-posed problem 98
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