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

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Ќазвание: Computational Techniques for Fluid Dynamics. Vol. 1

јвтор: Fletcher C.A.


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.

язык: en

–убрика: ‘изика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

»здание: Second edition

√од издани€: 1991

 оличество страниц: 401

ƒобавлена в каталог: 23.10.2007

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ѕредметный указатель
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 88Ч92 95 97 104 108 235 236
Accuracy of solution and grid refinement      89
Accuracy of solution and Richardson extrapolation      90Ч92
Accuracy of solution with Neumann boundary conditions      238Ч240
Accuracy of spectral method      146 149
Accuracy on a nonuniform grid      350Ч352
Adaptive grid techniques (reference)      352
Advantages of CFD      1Ч6
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      252Ч253
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      62Ч64 289Ч290
Amplitude ratio, one-dimensional transport equation      314 315
Approximate factorisation      254Ч256
Approximate factorisation and 2D Burgers' equation      362Ч364
Approximate factorisation and 2D diffusion equation      251Ч256
Approximate factorisation and 2D transport equation      317 318
Approximate factorisation and finite element methods      256Ч259
Approximate factorisation and Neumann boundary condition implementation      267Ч271
Approximate factorisation and pseudotransient method      208 209
Approximate factorisation and the role of mass operators      258
Approximate functions for finite element method      116Ч126
Approximate functions for spectral method      145Ч146
Approximate functions for weighted residual methods      99Ч101
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      98Ч105
Back-substitution      180 182 184 185
BANFAC: factorise tridiagonal matrix      184Ч186
BANSOL: solution (back-substitution) of tridiagonal system      184Ч186
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 32Ч34 36 37Ч38 101 126 137
Boundary conditions, accuracy      133 238Ч240
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      236Ч238 267Ч271
Boundary conditions, spectral method      146 147 149Ч151
Boundary conditions, stability      83Ч85
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      339Ч348
Burgers' equation      332Ч374
Burgers' equation, one dimensional (1D)      12 332Ч352
Burgers' equation, one dimensional, accuracy on a nonuniform grid      351Ч352
Burgers' equation, one dimensional, exact solution for      339
Burgers' equation, one dimensional, explicit schemes for      334Ч336
Burgers' equation, one dimensional, implicit schemes for      337Ч338
Burgers' equation, one dimensional, inviscid      332
Burgers' equation, one dimensional, low dispersion schemes for      345 348
Burgers' equation, one dimensional, physical behaviour      332Ч334
Burgers' equation, one dimensional, stationary      351
Burgers' equation, two dimensional (2D)      164 357Ч372
Burgers' equation, two dimensional, exact solution      361Ч362
Burgers' equation, two dimensional, split schemes for      362Ч364
Cell Reynolds number      294Ч298 324 325
Cell Reynolds number, oscillatory solution      295
CFD-geophysical      16
CFD-meteorological      16
CFL condition      278
Characteristic polynomial      27Ч30
Characteristics      18 21Ч28 30 32Ч40
Characteristics, method of      38Ч40
Chebyshev acceleration of iterative schemes (reference)      193 194
Chebyshev polynomial      146 152 153
CN-4PU scheme and 1D Burgers' equation      346Ч348
CN-4PU scheme and 1D transport equation      307 312Ч315
CN-FDM scheme and 1D Burgers' equation      343 346Ч348
CN-FDM scheme and 1D transport equation      307 312Ч315
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 313Ч315
Cole Ч 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 16Ч18 107 353Ч355
Compressible flow, inviscid      353Ч355
Computational efficiency and operation count estimates      92Ч94
Computer, architecture      5
computer, hardware      4
Computer, speed      4Ч7
Conjugate gradient method      200
Conjugate gradient method as an acceleration technique      201Ч203
Connectivity      358Ч359
Conservation form of Burgers' equation      333
Conservation of energy      11
Conservation of mass      11 38 107
Conservation of momentum      11
Consistency      73 75Ч79
Consistency and modified equation method      290
Consistency of DuFort Ч Frankel scheme      220 221
Consistency of FTCS scheme      77Ч78
Consistency of fully implicit scheme      78
Consistency, connection with truncation error      77Ч78
Continuity equation      34 105
Convection      11 12 276
Convection diffusion equation      293Ч298
Convection diffusion equation and cell Reynolds number      294Ч296
Convection diffusion equation and nonuniform grid accuracy      349Ч350
Convection diffusion equation and oscillatory solution      294Ч295
Convection equation, linear      31 277Ч286
Convection equation, linear, algebraic schemes for      278Ч279
Convection equation, linear, numerical algorithms for      277Ч283
Convection equation, linear, sine wave propagation      284Ч286
Convective nonlinearity      331
Convective nonlinearity, cubic      359
Convective nonlinearity, quadratic      359
Convective term, asymmetric discretisation      276
Convergence      58 73Ч76
Convergence, Newton's method      165 170 176
Convergence, numerical      58 60 75Ч76 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      22Ч23
Correction storage (CS) method      206; see also УMultigrid methodФ
Cost of software and hardware      3Ч6
COUNT program to obtain basic operation execution time      375
Courant (CFL) number      278
Crank Ч Nicolson scheme and four-point upwind scheme      305
Crank Ч Nicolson scheme and mass operator method      305
Crank Ч Nicolson scheme and Richardson extrapolation      90
Crank Ч Nicolson scheme for 1D Burgers' equation      337 338
Crank Ч Nicolson scheme for 1D diffusion scheme      228Ч229
Crank Ч Nicolson scheme for 1D transport equation      304Ч305
Crank Ч Nicolson scheme for linear convection equation      283 284 286 291
Crank Ч Nicolson scheme for systems of equations      353Ч355
Crank Ч Nicolson scheme, generalised for 1D Burgers' equation      338 339
Crank Ч Nicolson scheme, generalised for 2D diffusion scheme      261
Cross-stream diffusion      317 326Ч327
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      222Ч227 236
DIFF: elementary finite difference program      66Ч68
Difference operators      376Ч379
Difference operators, directional      377
Diffusion equation, one dimensional (1D)      34 40 65 135 146Ч149 216Ч241
Diffusion equation, one dimensional (1D), algebraic schemes for      219
Diffusion equation, one dimensional (1D), explicit methods for      217Ч222 226
Diffusion equation, one dimensional (1D), implicit methods for      227Ч231
Diffusion equation, one dimensional (1D), separation of variables solution      67
Diffusion equation, two dimensional (2D)      249Ч251
Diffusion equation, two dimensional (2D) and ADI method      252Ч253
Diffusion equation, two dimensional (2D) and approximate factorisation method      254Ч256
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      251Ч259
Diffusion, numerical      281 285
Diffusion, physical      11 12
DIFIM: implicit schemes applied to the diffusion scheme      231Ч236
Direct Poisson solvers      190Ч192
Direct solution methods for linear algebraic systems      164 180Ч182
Dirichlet boundary conditions      20 36 37 108
Discretisation      15 47Ч60 136
Discretisation and ordinary differential equation connection      51
Discretisation and solution smoothness      58Ч60
Discretisation and wave representation      61Ч64
Discretisation of derivatives by general technique      53Ч55
Discretisation of derivatives by Taylor series expansion      52Ч53
Discretisation of spatial derivatives      49
Discretisation of time derivatives      50Ч51
Discretisation, accuracy      55Ч64
Discretisation, accuracy and truncation error      56Ч58
Discretisation, accuracy for first derivatives      56Ч58
Discretisation, accuracy for second derivatives      56Ч58
Discretisation, accuracy via Fourier analysis      62Ч64
Discretisation, grid coarseness      61
Discretisation, higher-order formulae      58Ч60 63Ч64
Discriminant      22 23 25
Dispersion wake      286
Dispersion, numerical      286Ч292
Dispersion, numerical and 2D transport equation      317
Dispersion, numerical and Fourier analysis      288Ч290 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 304Ч306
Dissipation of a plane wave      287
Dissipation, artificial      341 348
Dissipation, numerical      286Ч292
Dissipation, physical      31 43 59
Divergence form of the governing equations      333
Douglas Ч Gunn splitting algorithm      255
DUCT: viscous flow in a rectangular duct      137Ч143 194Ч195
DuFort Ч Frankel scheme      220Ч221 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 21Ч23 25Ч27 29 36Ч38 42Ч46
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      285Ч286
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      334Ч337 346Ч347
Explicit schemes for 1D diffusion equation      217Ч227
Explicit schemes for 1D transport equation      299Ч303
Explicit schemes for 2D diffusion equation      250Ч251
Explicit schemes for 2D transport equation      316Ч317
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      180Ч182
Factorisation, approximate      254
Fast Fourier Transform      153 156
Finite difference discretisation      47Ч53 56Ч60
Finite difference method      13Ч15 64Ч69 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 116Ч145 256Ч266
Finite element method and bilinear interpolation      121Ч122 125
Finite element method and biquadratic interpolation      123Ч126
Finite element method and diffusion equation      135Ч136
Finite element method and discretisation      48Ч50 129 136 139
Finite element method and interpolation      116
Finite element method and linear interpolation      117Ч119
Finite element method and Poisson equation      137Ч138
Finite element method and quadratic interpolation      119Ч121
Finite element method and Sturm Ч Liouville equation      126Ч135
Finite elements      121Ч123 126
Finite volume method      15 105Ч116
Finite volume method and discretisation      48
Finite volume method and first derivatives      105Ч107
Finite volume method and Laplace's equation      111Ч116
Finite volume method and second derivatives      107Ч111
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      111Ч115
Flat plate solar collector      166 167
Flow separation      8
Four point upwind scheme      296Ч298; see also УUpwind schemeФ
Fourier (stability) analysis      80 85Ч88
Fourier (stability) analysis for 1D transport equation      310 314Ч315
Fourier (stability) analysis for linear convection equation      288Ч290
Fourier analysis, pde classification      28Ч30
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 217Ч220 226 236 239
FTCS scheme and Burgers' equation      334 346
FTCS scheme and Euler schemes      243
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