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Fletcher C.A. — Computational Techniques for Fluid Dynamics. Vol. 1
Fletcher C.A. — Computational Techniques for Fluid Dynamics. Vol. 1



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Íàçâàíèå: Computational Techniques for Fluid Dynamics. Vol. 1

Àâòîð: Fletcher C.A.

Àííîòàöèÿ:

This well-known 2-volume textbook provides senior undergraduate and postgraduate engineers, scientists and applied mathematicians with the specific techniques, and the framework to develop skills in using the techniques in the various branches of computational fluid dynamics.
Volume 1 systematically develops fundamental computational techniques, partial differential equations including convergence, stability and consistency and equation solution methods. A unified treatment of finite difference, finite element, finite volume and spectral methods, as alternative means of discretion, is emphasized. For the second edition the author also compiled a separately available manual of solutions to the many exercises to be found in the main text.


ßçûê: en

Ðóáðèêà: Ôèçèêà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Èçäàíèå: Second edition

Ãîä èçäàíèÿ: 1991

Êîëè÷åñòâî ñòðàíèö: 401

Äîáàâëåíà â êàòàëîã: 23.10.2007

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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Ïðåäìåòíûé óêàçàòåëü
A, $A(\alpha)$ 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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