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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 |
FTCS scheme and linear convection equation 277 278
FTCS scheme and Richardson extrapolation 91
FTCS scheme, and 2D diffusion equation 250
FTCS scheme, fourth-order accuracy 77
FTCS scheme, stability of 81—82 85—86
Fully implicit scheme for diffusion equation 227—228
Galerkin (weighted residual) method 101—104 377
Galerkin finite element method 126—144 355—359
Galerkin finite element method, boundary implementation 269
Galerkin spectral method 147 150
Gauss elimination 152 180—183
Gauss elimination, narrowly banded 184—186
Gauss elimination, sparse 182—183
Gauss quadrature 145
Gauss — Seidel iterative method 193—196
General three-level scheme for 1D diffusion equation 229 230
General three-level scheme for 2D diffusion equation 255
Generalised coordinates 22 43 107 156
Global constraint and elliptic partial differential equation 38
Global method vs local method 14 15 145 156
Green's function method 41—42
Green's theorem 38
Grid generation 7 8
Grid growth ratio 349 377
Grid nonuniformity and solution accuracy 348—352
Grid nonuniformity and solution accuracy and truncation error 349 350
Grid refinement and accuracy 58—61 75 89—92 119 121 134 143 226 235—240 266
Grid refinement and iterative convergence 192 195 198
Group finite element method 355—360
Group finite element method and 1D Burgers' equation 340
Group finite element method, and 2D transport equation 319—320
Group finite element method, comparison with conventional finite element method 358—360
Group finite element method, computational efficiency 356
Group finite element method, one-dimensional formulation 356
Group finite element method, operation count for 358—359
Group finite element method, two-dimensional formulation 357—358
Heat conduction equation 34 48 64—66 135 216—217
Higher order difference formulae 58—60 63—64
Higher order explicit schemes for diffusion equation 221 226
Higher order implicit schemes for diffusion equation 230 231
Hopscotch method 251
Hyperbolic partial differential equation 17—19 21—23 25—27 30—38 43—45
Hyperbolic partial differential equation1 and discontinuity propagation 89
Hyperbolic partial differential equation1, boundary conditions for 32—34
Hyperbolic partial differential equation1, characteristics for 30—31
Hyperbolic partial differential equation1, domains of dependence and influence 31
Hyperbolic partial differential equation1, initial conditions for 31
Ill-conditioned system of equations 186
Implicit schemes for diffusion equation 228—236
Implicit schemes for the 1D Burgers' equation 337—339
Implicit schemes for the 1D transport equation 304—306
Implicitness parameter 82 87 136
Initial conditions 19 20 241
Instability, nonlinear 154
Instability, nonlinear, physical 88
Integral form, governing equation 106
Interpolation 116—126
Interpolation, bilinear 121—122 125 144
Interpolation, biquadratic 123—125
Interpolation, error 119 121 125
Interpolation, function 118 120 121—123 377
Interpolation, higher-order 121 126 134
Interpolation, linear 117—119 134
Interpolation, multigrid 204—207
Interpolation, quadratic 119—121 134
Inviscid Burgers' equation 332 333 335 337
Inviscid flow 7—8 13 16 18—20 30 32—33 44—45 59 116 353—355
Isoparametric formulation 143—145
Iterative methods for algebraic systems of equations 192—207
Iterative methods for algebraic systems of equations, convergence acceleration 200—207
Iterative methods for algebraic systems of equations, convergence acceleration via iterative sequence 197 214 215
Iterative methods for algebraic systems of equations, convergence rate and grid refinement 198
Iterative methods for algebraic systems of equations, convergence rate and strong ellipticity 198
Iterative methods for algebraic systems of equations, Gauss — Seidel method 193
Iterative methods for algebraic systems of equations, general structure 192
Iterative methods for algebraic systems of equations, implicit algorithms 196—200
Iterative methods for algebraic systems of equations, Jacobi method 193
Iterative methods for algebraic systems of equations, point vs line methods 195
Iterative methods for algebraic systems of equations, SLOR method 197
Iterative methods for algebraic systems of equations, SOR method 193
JACBU: evaluates Jacobian of 2D Burgers' equations 177 211
JACOB: evaluates Jacobian required by Newton's method 169 170
Jacobi iterative method 193—197
Jacobi iterative method and pseudotransient method 208
Jacobian, Newton 165 169 170 172 211 212
Jacobian, transformation 23 145
Korteweg de Vries equation 44
Lagrange interpolation function 120 123 124 126
Laplace's equation 13 107—116
Lax equivalence theorem 74
Lax — Wendroff scheme and 1D transport equation 301 303 307 312
Lax — Wendroff scheme and linear convection equation 281—283 291—292
Lax — Wendroff scheme and systems of equations 353—355
Lax — Wendroff scheme, two-stage 335 336 346 353—354
Leapfrog scheme for linear convection equation 281 282
Least-squares (weighted residual) method 100 103
Leith's scheme 282
Locally one-dimensional method 272; see also “Method of fractional steps”
LU-factorisation and Gauss elimination 169
LU-factorisation, incomplete 207
MacCormack scheme, explicit 354
Mach number 18
MACSYMA, symbolic manipulation 291
Mass operator and bilinear interpolation 256
Mass operator and Galerkin weighted integral 378
Mass operator and linear interpolation and fourth-order accuracy 379
Mass operator and Pade differencing 379
Mass operator and three dimensional discretisation 379
Mass operator, boundary evaluation 270—271
Mass operator, computational scheme 307 338 362 376—379
Mass operator, directional 136 138 139 377
Mass operator, generalised 231 260 283 305 317 325 338 362
Mass operator, generalised and dispersion 305 345
Matrix, banded 163
Matrix, dense 163
Matrix, diagonal dominance 192
Matrix, fill-in 182
Matrix, positive definite 179
Matrix, sparse 163 182
Matrix, spectral radius 192
Matrix, structure for finite difference scheme 163
Maximum principle for elliptic partial differential equations 37
Megaflop 4 6
Method of characteristics 38—40
Method of fractional steps 271—273
Method of lines and ordinary differential equations 241—246
Microcomputers and CFD 6
Minicomputers and CFD 6
Modified equation method 290—291
Modified equation method and 1D transport equation 305 306
Modified equation method, and 2D transport equation 324
Multigrid method 203—207 211
Multigrid method and prolongation (interpolation) operator 204
Multigrid method and restriction operator 204—205
Multigrid method and V-cycle 205
Multigrid method, correction storage (CS) for linear problems 206
Multigrid method, full (FMG) 207
Multigrid method, problems 207
Multistep-method, linear for ordinary differential equations 242
Navier — Stokes equations 19—20 28 35 37 43
Navier — Stokes equations, reduced form 1 8 28
Navier — Stokes equations, thin layer form 8
Neumann boundary conditions 20 36—38 236—241
Neumann boundary conditions and accuracy 133 238—240 268
Neumann boundary conditions and finite volume method 111
Neumann boundary conditions and spectral method 149
Neumann boundary conditions and splitting 266—271
Neumann boundary conditions and stability 83—85
Neumann boundary conditions, finite difference implementation 267—268
Neumann boundary conditions, finite element implementation 269—271
| Neumann boundary conditions, numerical implementation 237—238
NEWTBU, inclusion of augmented Jacobian 210—211
NEWTBU: two dimensional Burgers' equation 171—179
Newton's method 163—166
NEWTON: flat plate collector analysis 166—170
Nondimensionalisation 12 148
Numerical dissipation and dispersion 287—293
Numerical dissipation and modified equation method 290—291
Numerical dissipation, dispersion and discretisation schemes 292
Numerical dissipation, dispersion and Fourier analysis 288—290
One-sided differencing 50 54
Operation count and block Thomas algorithm 189
Operation count and finite element method 358 359
Operation count, empirical determination 92—94
Optimal-rms solution and weighted residual method 103
Ordinary differential equations 241—246
Ordinary differential equations and absolute stability 244
Ordinary differential equations and linear multistep methods 242—243
Ordinary differential equations and Runge — Kutta schemes 243—245
Orthogonal collocation 95 100 156
Orthogonal function 146 147
ORTHOMIN algorithm 202
Panel method 182
Parabolic partial differential equation 17 18 21—23 25—26 34—38
Parabolic partial differential equation, boundary conditions for 36
Parallel processing 5 6 16
Partial differential equations (PDE) 17—42
Partial differential equations (pde) and coordinate transformation 22—23
Partial differential equations (pde) and symbol 29
Partial differential equations (pde), boundary and initial conditions for 18—20
Partial differential equations (pde), classification by characteristics 17 21—24
Partial differential equations (pde), classification by symbol (Fourier) analysis 28—30
Partial differential equations (pde), first-order 21 24
Partial differential equations (pde), linear 12
Partial differential equations (pde), principal part 28
Partial differential equations (pde), second order 17 21
Partial differential equations (pde), system of equations 24—28
Peclet number 294 305
Pentadiagonal systems of equations/matrix 131 185—188
Phase error 63
Phase, change of 289
Pipeline architecture 4 5
Pivoting, partial and Gauss elimination 180
Plane-wave propagation 287
Point source 41
Poisson equation 37—38 41—42 137
Poisson solvers, direct 190—192
potential flow 36
Power method for maximum eigenvalue determination 84
Prandtl number 319
Preconditioned conjugate gradient method 201—203
Predictor corrector scheme for ordinary differential equations 243
Primitive variables 34
Product approximation 360
Prolongation operator 204—206; see also “Multigrid method”
Pseudospectral method 151—154
Pseudospectral method in physical space 154—156
Pseudotransient method 208—212
Pseudotransient method and 2D steady Burgers' equation 209
Pseudotransient method and Newton's method 210
Pseudotransient method, comparison with Jacobi iteration 208
Quadridiagonal matrix 297 338
Quadridiagonal matrix and the Thomas algorithm 297 306
Quasi-Newton method 179
RESBU: evaluates residuals of 2D Burgers' equations 176
RESID: evaluates residuals required by Newton's method 169
Residual, equation 99 104 127 146 176
Residual, equation and multigrid method 203—207
Residual, equation, evaluation for finite element method 261 266
Restriction operator 204; see also “Multigrid method”
Reynolds number 2 8 27 59 294 305 319 325 339 369
RHSBU: evaluates right-hand side of Burgers' equations 370
Richardson extrapolation 89—92 241
Richardson extrapolation and operation count 91—92
Richardson extrapolation, active 91
Richardson extrapolation, passive 91
Richardson scheme 220
Robin boundary condition 20
Round-off error 74 79 80 86
Runge — Kutta method 242—245
Runge — Kutta method, explicit 242 244
Runge — Kutta method, implicit 243
Search direction and modified Newton's method 176
Semi-discrete form of partial differential equations 242
Separation of variables method 40—41
Serendipity elements 126
Shape (interpolation) functions 117
Shock formation 332
Shock wave 7 32 43
Shock wave and stationary Burgers' equation 351 352
Shock wave, propagation 353—355
Shock wave, propagation and Burgers' equation 339 346—348 357
Smoothness of solution and accuracy of representation 58 60 61 236
Spectral method 11 15 16 47 48 50 98 99 104 145—156 182
Spectral method and Burgers' equation 348
Spectral method and diffusion equation 146—149
Spectral method and Neumann boundary conditions 149—151
Spectral method and nonlinear terms 149
Spectral method in physical space 154
Splitting see “Approximate factorisation”
Stability 15 55 73—75 79—88
Stability of ADI scheme 253
Stability of convection equation schemes 278 279
Stability of diffusion equation schemes 219
Stability of three-level scheme for 1D diffusion scheme 222
Stability of transport equation schemes 302 303
Stability, absolute for ordinary differential equations 244
Stability, at boundaries 88 238
Stability, matrix method and FTCS scheme 81
Stability, matrix method and generalised two-level scheme 82
Stability, matrix method and Neumann boundary-conditions 83—85
Stability, polynomial for ordinary differential equations 244
Stability, von Neumann method and FTCS scheme 85—86
Stability, von Neumann method and generalised two-level scheme 86—88
Steady flow problems, overall strategy 211 212
Stiff systems of equations 229 246
Stiff systems of equations and steady-state convergence 229 230
Streamline diffusion (artificial) 327
Strongly implicit procedure (SIP) 198—199
Strongly implicit procedure (SIP), modified (MSI) algorithm 199—200
Sturm — Liouville equation 126—135
STURM: computation of the Sturm — Liouville equation 130—134
Subdomain method 100 103 105 106 108
Successive over-relaxation (SOR) iterative method 111 139 193—198
Supercomputer 2
Supersonic flow 7 8 18 30 59
Symmetric SOR (SSOR) iterative method 194
System of algebraic equations 163—164
System of algebraic equations, nonlinear 164
System of governing equations 24—28 331 353—355
Tau method 151
Taylor series expansion 52
Taylor weak statement (TWS) of finite element method 292
Taylor — Galerkin finite element method 292
Temperature 3 11 12 48 65 166 277 305 318
Temperature front convection 305—306 312 313
Tensor product 138 139 256 377
Term-by-term finite element discretisation 136 139
Test function 100
TEXCL: semi-exact centreline solution 320 325
THERM: thermal entry problem 318—326
Thermal diffusivity 48 82
Thomas algorithm 130 136 183—184
Thomas algorithm and line iteration method 194
Thomas algorithm, block 188—189
Thomas algorithm, generalised 187—188
Three level explicit scheme 221 226
Three level fully implicit scheme 227
Three level generalised implicit scheme 229
TRAN: convection of a temperature front 305—316
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