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Ïîèñê ïî óêàçàòåëÿì |
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Fletcher C.A. — Computational Techniques for Fluid Dynamics. Vol. 1 |
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Ïðåäìåòíûé óêàçàòåëü |
A, stability of ordinary differential equations 246
Acceleration, Chebyshev 193
Acceleration, conjugate gradient 193
Accuracy and grid coarseness 61 111 134 235
Accuracy and interpolation 119 121 125 134
Accuracy of solution 58 73 88—92 95 97 104 108 235 236
Accuracy of solution and grid refinement 89
Accuracy of solution and Richardson extrapolation 90—92
Accuracy of solution with Neumann boundary conditions 238—240
Accuracy of spectral method 146 149
Accuracy on a nonuniform grid 350—352
Adaptive grid techniques (reference) 352
Advantages of CFD 1—6
AF-4PU scheme 325 326 369 371 372
AF-FDM scheme 325 326 369 371 372
AF-FEM scheme 325 326
AF-MO scheme 369 371 372
Algebraic grid generation 8
Aliasing 154 334
Alternating direction implicit (ADI) method for steady problems 197
Alternating direction implicit (ADI) method for transient problems 252—253
Alternating direction implicit (ADI) method in three dimensions 253
Alternating direction implicit (ADI) method, finite element algorithm 258
Amdahl's Law 4 5
Amplification factor and stability 86
Amplification matrix and systems of equations 354
Amplitude error 63
Amplitude of Fourier mode 61
Amplitude ratio, discretisation accuracy 62—64 289—290
Amplitude ratio, one-dimensional transport equation 314 315
Approximate factorisation 254—256
Approximate factorisation and 2D Burgers' equation 362—364
Approximate factorisation and 2D diffusion equation 251—256
Approximate factorisation and 2D transport equation 317 318
Approximate factorisation and finite element methods 256—259
Approximate factorisation and Neumann boundary condition implementation 267—271
Approximate factorisation and pseudotransient method 208 209
Approximate factorisation and the role of mass operators 258
Approximate functions for finite element method 116—126
Approximate functions for spectral method 145—146
Approximate functions for weighted residual methods 99—101
Approximate solution 47 49 73 74 76 377
Approximate solution for finite element method 126 127
Approximate solution for spectral method 146
Approximate solution for weighted residual methods 98—105
Back-substitution 180 182 184 185
BANFAC: factorise tridiagonal matrix 184—186
BANSOL: solution (back-substitution) of tridiagonal system 184—186
BFGS algorithm (quasi-Newton method) 179
Biconjugate gradient method 203
Block Thomas algorithm 189
Block tridiagonal system of equations 188 189
boundary conditions 19 20 32—34 36 37—38 101 126 137
Boundary conditions, accuracy 133 238—240
Boundary conditions, diffusion equation 48 135 146 152 216 217
Boundary conditions, Dirichlet 20
Boundary conditions, finite element method 127
Boundary conditions, Neumann 20
Boundary conditions, numerical implementation 236—238 267—271
Boundary conditions, spectral method 146 147 149—151
Boundary conditions, stability 83—85
Boundary formulation of the finite element method 131
Boundary layer 35 293
Boundary, initial condition interaction, accuracy of 68 69
BURG: numerical comparison for 1D Burgers' equation 339—348
Burgers' equation 332—374
Burgers' equation, one dimensional (1D) 12 332—352
Burgers' equation, one dimensional, accuracy on a nonuniform grid 351—352
Burgers' equation, one dimensional, exact solution for 339
Burgers' equation, one dimensional, explicit schemes for 334—336
Burgers' equation, one dimensional, implicit schemes for 337—338
Burgers' equation, one dimensional, inviscid 332
Burgers' equation, one dimensional, low dispersion schemes for 345 348
Burgers' equation, one dimensional, physical behaviour 332—334
Burgers' equation, one dimensional, stationary 351
Burgers' equation, two dimensional (2D) 164 357—372
Burgers' equation, two dimensional, exact solution 361—362
Burgers' equation, two dimensional, split schemes for 362—364
Cell Reynolds number 294—298 324 325
Cell Reynolds number, oscillatory solution 295
CFD-geophysical 16
CFD-meteorological 16
CFL condition 278
Characteristic polynomial 27—30
Characteristics 18 21—28 30 32—40
Characteristics, method of 38—40
Chebyshev acceleration of iterative schemes (reference) 193 194
Chebyshev polynomial 146 152 153
CN-4PU scheme and 1D Burgers' equation 346—348
CN-4PU scheme and 1D transport equation 307 312—315
CN-FDM scheme and 1D Burgers' equation 343 346—348
CN-FDM scheme and 1D transport equation 307 312—315
CN-FEM scheme and 1D Burgers' equation 343 346 347
CN-FEM scheme and 1D transport equation 307 312 313
CN-FEM(C) scheme 356 357
CN-FEM(G) scheme 357
CN-MO scheme and 1D Burgers' equation 343 347 348
CN-MO scheme and 1D transport equation 307 309 313—315
Cole — Hopf transformation 333 361
Collocation, (weighted residual) method 100 103 104
Collocation, orthogonal 95 100 156
Collocation, spectral (pseudospectral) method 151 154
Compatibility condition (method of characteristics) 31 38
Compressible flow 7 13 16—18 107 353—355
Compressible flow, inviscid 353—355
Computational efficiency and operation count estimates 92—94
Computer, architecture 5
computer, hardware 4
Computer, speed 4—7
Conjugate gradient method 200
Conjugate gradient method as an acceleration technique 201—203
Connectivity 358—359
Conservation form of Burgers' equation 333
Conservation of energy 11
Conservation of mass 11 38 107
Conservation of momentum 11
Consistency 73 75—79
Consistency and modified equation method 290
Consistency of DuFort — Frankel scheme 220 221
Consistency of FTCS scheme 77—78
Consistency of fully implicit scheme 78
Consistency, connection with truncation error 77—78
Continuity equation 34 105
Convection 11 12 276
Convection diffusion equation 293—298
Convection diffusion equation and cell Reynolds number 294—296
Convection diffusion equation and nonuniform grid accuracy 349—350
Convection diffusion equation and oscillatory solution 294—295
Convection equation, linear 31 277—286
Convection equation, linear, algebraic schemes for 278—279
Convection equation, linear, numerical algorithms for 277—283
Convection equation, linear, sine wave propagation 284—286
Convective nonlinearity 331
Convective nonlinearity, cubic 359
Convective nonlinearity, quadratic 359
Convective term, asymmetric discretisation 276
Convergence 58 73—76
Convergence, Newton's method 165 170 176
Convergence, numerical 58 60 75—76 116 134 226 235 236 239 240
Convergence, numerical, for 2D Burgers' equation 359 360
Convergence, numerical, pseudotransient Newton's method 210
Convergence, numerical, quadratic for Newton's method 165 170
Convergence, numerical, radius of 166 179
Convergence, numerical, rate 76 78 116 134 226 235 236 239 240
Convergence, numerical, rate of iteration and strong ellipticity 198
Convergence, numerical, rate, numerical 235 236 239 240
Coordinate system, element based 121 124 127
Coordinate system, element based, generalised 352
Coordinate transformation 22—23
Correction storage (CS) method 206; see also “Multigrid method”
| Cost of software and hardware 3—6
COUNT program to obtain basic operation execution time 375
Courant (CFL) number 278
Crank — Nicolson scheme and four-point upwind scheme 305
Crank — Nicolson scheme and mass operator method 305
Crank — Nicolson scheme and Richardson extrapolation 90
Crank — Nicolson scheme for 1D Burgers' equation 337 338
Crank — Nicolson scheme for 1D diffusion scheme 228—229
Crank — Nicolson scheme for 1D transport equation 304—305
Crank — Nicolson scheme for linear convection equation 283 284 286 291
Crank — Nicolson scheme for systems of equations 353—355
Crank — Nicolson scheme, generalised for 1D Burgers' equation 338 339
Crank — Nicolson scheme, generalised for 2D diffusion scheme 261
Cross-stream diffusion 317 326—327
Cycle time, computer 4 5
Cyclic reduction for Poisson equation 190 191
Deferred correction method 95
Degenerate system of partial differential equations 26 27
Design and CFD 1 2 5
DIFEX: explicit schemes applied to diffusion equation 222—227 236
DIFF: elementary finite difference program 66—68
Difference operators 376—379
Difference operators, directional 377
Diffusion equation, one dimensional (1D) 34 40 65 135 146—149 216—241
Diffusion equation, one dimensional (1D), algebraic schemes for 219
Diffusion equation, one dimensional (1D), explicit methods for 217—222 226
Diffusion equation, one dimensional (1D), implicit methods for 227—231
Diffusion equation, one dimensional (1D), separation of variables solution 67
Diffusion equation, two dimensional (2D) 249—251
Diffusion equation, two dimensional (2D) and ADI method 252—253
Diffusion equation, two dimensional (2D) and approximate factorisation method 254—256
Diffusion equation, two dimensional (2D), explicit methods for 250
Diffusion equation, two dimensional (2D), generalised implicit scheme 254
Diffusion equation, two dimensional (2D), implicit methods for 251
Diffusion equation, two dimensional (2D), splitting methods for 251—259
Diffusion, numerical 281 285
Diffusion, physical 11 12
DIFIM: implicit schemes applied to the diffusion scheme 231—236
Direct Poisson solvers 190—192
Direct solution methods for linear algebraic systems 164 180—182
Dirichlet boundary conditions 20 36 37 108
Discretisation 15 47—60 136
Discretisation and ordinary differential equation connection 51
Discretisation and solution smoothness 58—60
Discretisation and wave representation 61—64
Discretisation of derivatives by general technique 53—55
Discretisation of derivatives by Taylor series expansion 52—53
Discretisation of spatial derivatives 49
Discretisation of time derivatives 50—51
Discretisation, accuracy 55—64
Discretisation, accuracy and truncation error 56—58
Discretisation, accuracy for first derivatives 56—58
Discretisation, accuracy for second derivatives 56—58
Discretisation, accuracy via Fourier analysis 62—64
Discretisation, grid coarseness 61
Discretisation, higher-order formulae 58—60 63—64
Discriminant 22 23 25
Dispersion wake 286
Dispersion, numerical 286—292
Dispersion, numerical and 2D transport equation 317
Dispersion, numerical and Fourier analysis 288—290 314 315
Dispersion, numerical and truncation error 297 298 300 305
Dispersion, numerical of a plane wave 287
Dissipation and 2D transport equation 326
Dissipation and truncation error 298 300 304—306
Dissipation of a plane wave 287
Dissipation, artificial 341 348
Dissipation, numerical 286—292
Dissipation, physical 31 43 59
Divergence form of the governing equations 333
Douglas — Gunn splitting algorithm 255
DUCT: viscous flow in a rectangular duct 137—143 194—195
DuFort — Frankel scheme 220—221 226 301 302
Efficiency, computational 58
Eigenvalue 23 81 83 84 245
Eigenvalue and oscillatory solution 294 295
Eigenvalue, annihilation and conjugate gradient method 201
Eigenvalue, maximum and the power method 84
Element-based coordinates 378
Elliptic partial differential equation 17 18 21—23 25—27 29 36—38 42—46
Elliptic partial differential equation, boundary and integral conditions for 38
Energy method of stability analysis (reference) 94
ERFC: complementary error function evaluation 344
Error growth and stability 79 81 85 86
Error of solution 74 89 90 92 94 102 104 121 130 134 143
Error of solution and 1D Burgers' equation 346 347 371 372
Error of solution and 1D diffusion equation 226 235 236
Error of solution and 1D transport equation 312 313
Error of solution and 2D diffusion equation 266
Error of solution and 2D transport equation 326
Error of solution and convection diffusion equation 298
Error of solution and linear convection equation 285—286
Error of solution and mixed Dirichlet/Neumann boundary condition 268
Error of solution and Neumann boundary conditions 239 240
Euler discretisation scheme 51 152 242
Euler discretisation scheme, stability restriction 245
Euler equations 8 353
EX-4PU scheme for 1D transport equation 307
EXBUR: exact solution of 2D Burgers' equation 175
Execution time for basic operations 375
Explicit schemes for 1D Burgers' equation 334—337 346—347
Explicit schemes for 1D diffusion equation 217—227
Explicit schemes for 1D transport equation 299—303
Explicit schemes for 2D diffusion equation 250—251
Explicit schemes for 2D transport equation 316—317
EXSH: exact solution of 1D Burgers' equation 344
EXSOL: exact solution of 1D transport equation 311
EXTRA: exact solution of 1D diffusion equation 222 225
FACR algorithm 191
FACT/SOLVE: solution of dense systems of algebraic equations 180—182
Factorisation, approximate 254
Fast Fourier Transform 153 156
Finite difference discretisation 47—53 56—60
Finite difference method 13—15 64—69 92 95 100 143
Finite difference method and matrix structure 163
Finite difference operators 138 228 230 250 270 279 303 335
Finite element method 15 116—145 256—266
Finite element method and bilinear interpolation 121—122 125
Finite element method and biquadratic interpolation 123—126
Finite element method and diffusion equation 135—136
Finite element method and discretisation 48—50 129 136 139
Finite element method and interpolation 116
Finite element method and linear interpolation 117—119
Finite element method and Poisson equation 137—138
Finite element method and quadratic interpolation 119—121
Finite element method and Sturm — Liouville equation 126—135
Finite elements 121—123 126
Finite volume method 15 105—116
Finite volume method and discretisation 48
Finite volume method and first derivatives 105—107
Finite volume method and Laplace's equation 111—116
Finite volume method and second derivatives 107—111
Finite volume method, accuracy and grid refinement 116
Finite volume method, iterative convergence and grid refinement 116
First derivative operator and Galerkin weighted integral 378
FIVOL: finite volume method applied to Laplace's equation 111—115
Flat plate solar collector 166 167
Flow separation 8
Four point upwind scheme 296—298; see also “Upwind scheme”
Fourier (stability) analysis 80 85—88
Fourier (stability) analysis for 1D transport equation 310 314—315
Fourier (stability) analysis for linear convection equation 288—290
Fourier analysis, pde classification 28—30
Fourier representation of wave-like motion 61 62
Fourier series as approximating and weight functions 146
Fourier series method for Poisson equation 190 191
Fourier transform and symbol of pde 29
FTCS scheme 65 156 217—220 226 236 239
FTCS scheme and Burgers' equation 334 346
FTCS scheme and Euler schemes 243
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