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Transcript
References
Chapter 11
Aris, R. (1962): Vectors, Tensors and the Basic Equations of Fluid Dynamics (Prentice-Hall, Englewood Cliffs, N.J.)
Batchelor, G.K. (1967): An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge) Bird, G. (1976): Molecular Gas Dynamics (Oxford University Press, Oxford) Cebeci, T., Bradshaw, P. (1977): Momentum Transfer in Boundary Layers (Hemisphere- McGraw-Hill,
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(Springer, New York, Berlin, Heidelberg) Chu, C.K. (1978): Adv. App!. Mech. 18,285- 331 Crochet, M.J., Davis, A.R., Walters, K. (1984): Numerical Simulation of Non-Newtonian Flow (Elsevier,
Amsterdam) Eckert, E.R.G., Drake, R.M. (1972): Analysis of Heat and Mass Transfer (McGraw-Hill, New York) Gresho, P.M. (1991): "Incompressible Fluid Dynamics : Some Fundamental Formulation Issues", Annu.
Rev. Fluid Mech. 23 (to appear) Gustafson, K.E. (1980): Partial Differential Equations and Hilbert Space Methods (Wiley, New York) Gustafsson, B., Sundstrom, A. (1978): SIAM 1. App!. Math. 35, 343-357 Hughes, W.F., Gaylord, E.W. (1964): Basic Equations of Engineering Science (McGraw-Hill, New York) Hussaini, M.Y., Zang, T.A. (1987): Annu. Rev. Fluid Mech. 19, 339-367 Launder, B.E., Spalding, D.B. (1974): Com put. Methods App!. Mech. Eng. 3, 269-289 Liepmann, H.W., Roshko, A. (1957): Elements of Gasdynamics (Wiley, New York) Lighthill, M.J. (1963): In Laminar Boundary Layers, ed. by L. Rosenhead (Oxford University Press,
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E. Krause, Lecture Notes in Physics, Vo!' 170 (Springer, Berlin, Heidelberg) pp. 286-295 Launder, B.E., Spalding, D.B. (1974): Comput. Methods App!. Mech. Eng. 3, 269-289 Lombard, C.K., Bardina, 1., Venkatapathy, E., Yang, J.Y., Luh, R.C.e., Nagaraj, N., Raiszadeh, F. (1986):
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AIAA Paper 85-0032 MacCormack, R.W., Baldwin, B.S. (1975): A Numerical Method for Solving the Navier-Stokes
Equations with Application to Shock-Boundary Layer Interactions, AIAA Paper 75-1 MacCormack, R.W., Lomax, H. (1979): Annu. Rev. Fluid Mech. 11, 289-316 Mandella, M., Bershader, D. (1987): "Quantitative Study of the Compressible Vortices: Generation,
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on Triangular Meshes", AIAA 89-{)120 Morinishi, K., Satofuka, N. (1991): "Convergence Acceleration of a Rational Runge-Kutta Scheme for
Euler and Navier-Stokes Equations", Corn put. Fluids (to appear) Munz, e.-D. (1988): J. Comput. Phys. 77, 18-39 Obayashi, S., Kuwahara, K. (1986): J. Comput. Phys. 63, 157-167 Oran, E.S., Boris, J.P., Brown, E.F. (1990): "Fluid Dynamic Computations on a Connection
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(Springer, Berlin, Heidelberg) Peyret, R., Viviand, H. (1975): "Computation of Viscous Compressible Flow Based on the Navier
Stokes Equations", AGARDograph 212 Pulliam, T.H., Steger, J.L. (1980): AIAA J. 18, 159-167 Pulliam, T.H., Steger, J.L. (1985): "Recent Improvements in Efficiency, Accuracy and Convergence for
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in Physics, Vol. 170 (Springer, Berlin, Heidelberg) 507-512 Venkatakrishnan, V., Jameson, A. (1988): AIAA 1. 26,974--981 Venkatakrishnan, V., Saltz, J.H., Mavriplis, D.1. (1991): "Parallel Preconditioned Iterative Methods for
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89-D4, Von Karman Institute
Subject Index
The numbers I or II preceding the page numbers refer to the respective volume of Computational Techniques for Fluid Dynamics
A, A (a) stability of ordinary differential equations I 246
acceleration, Chebyshev I 193 acceleration, conjugate gradient I 193 accuracy - and grid coarseness I 61, 111, 134, 235 - and interpolation I 119, 121, 125, 134 - on a nonuniform grid I 350-352 - of solution I 58, 73, 88-92, 95, 97, 104,
108, 235, 236 - of solution and grid refinement
I 89; II 76 - of solution with Neumann boundary
conditions I 238 - 240 - of solution and Richardson extrapolation
I 90-92 - of spectral method I 146, 149 adaptive grid techniques (reference)
I 352; II 124 advantages of CFO I 1-7 alternating direction implicit (AD!) method - finite element algorithm I 258 - for steady problems I 197 - in three dimensions I 253 - for transient problems I 252-253 AF-FOM scheme I 325, 326, 369, 371, 372 AF-FEM scheme I 325, 326 AF-MO scheme I 369, 371, 372 AF-4PU scheme I 325, 326, 369, 371,
372 algebraic grid generation I 8; II 124 - multisurface technique II 108 - 11 2 - transfinite interpolation II 112-114 - two-boundary technique II 106- 108 ALGEM: algebraic grid generation for
streamlined body II 1 15- 123 aliasing I 154, 334; II 444 Amdahl's law I 4, 5 amplification factor and stability I 86 amplification matrix and systems of
equations I 354 amplitUde error I 63 amplitude of Fourier mode I 61 amplitude ratio, discretisation accuracy
I 62-64,289-290
amplitude ratio, one-dimensional transport equation I 314, 315
approximate factorisation I 254 - 256 - and artificial compressibility method
II 358 - Beam and Warming scheme II 421 -423 - compressible Navier-Stokes equations,
boundary conditions II 436-437 - FEM for vorticity transport equation
II 384 - and finite element methods I 256 - 259 - in generalised coordinates II 435,
438-440 - and group finite element method II 424,
438,439 - and Neumann boundary condition
implementation I 267-271 - and pseudotransient method I 208, 209 - and pseudotransient stream function
equation II 384 - and the role of mass operators I 258 - Samarskii and Andreev construction
II 376 - for transonic potential equation
II 194-195 - and 20 Burgers' equation I 362-364 - and 20 diffusion equation I 251 - 256 - and 20 transport equation I 317, 318 approximate functions - for finite element method I 116-126 - order for velocity, pressure (FEM)
interpolation II 370 - for spectral method I 145 - 146 - for weighted residual methods I 99-101 approximate solution I 47, 49, 73, 74, 76,
377 - for finite element method I 126, 127 - for spectral method I 146 - for weighted residual methods I 98 - 105 area vectors II 53, 59, 60 artificial compressibility method - and approximate factorisation II 357 - and artificial sound speed restriction
condition II 205 - laminar, Keller box scheme II 214-215
laminar, past a wedge II 207 - 209 - laminar, similarity variables II 207 - 209 - separation of II 24 - 26 - three-dimensional II 239-246 - turbulent II 22-24,221-239 - turbulent, Dorodnitsyn finite element
method II 223 - 226 - turbulent, Dorodnitsyn spectral method
II 237-239 - turbulent, Dorodnitsyn
transformation II 221 - 222 - 3D, Crank-Nicolson scheme II 242 - 3D, generalised coordinates II 243 - 244
- 3D, implicit split marching algorithm II 244-246
II 240-242 boundary, initial condition interaction,
accuracy of I 68, 69 BURG: numerical comparison for 10 Burgers'
equation I 339-348 Burgers' equation I 332-374 Burgers' equation, one dimensional (10)
I 12, 332-352 - accuracy on a nonuniform grid I 351-352 - exact solution for I 339 - explicit schemes for I 334-336 - implicit schemes for I 337 - 338 - inviscid I 332 - low dispersion schemes for I 345, 348 - physical behaviour I 332-334 - stationary I 351 Burgers' equation, two dimensional (20)
I 164,357-372 - exact solution I 361- 362 - split schemes for I 362-364
cell Reynolds number I 294-298, 324, 325; II 346
- oscillatory solution I 295 CFO-geophysical I 16 CFO-meteorological I 16 CFL condition I 278; II 344, 352 CFL condition, generalised II 147 C-grid and branch cuts II 88 characteristic decomposition for 10 Euler
equations II 448 characteristic polynomial I 27 - 30 characteristic polynomial analysis and symbolic
analysis II 263 characteristics I 18, 21-28, 30, 32-40 - method of I 38-40 Chebyshev acceleration of iterative schemes
(reference) I 193, 194 Chebyshev polynomial I 146, 152, 153 Chebyshev pseudospectral matrix (CPSM)
method II 349-355 CN-FOM scheme - and 10 Burgers' equation I 343, 346-348 - and 10 transport equation I 307,
312-315 CN-FEM scheme - and 10 Burgers' equation I 343, 346, 347 - and 10 transport equation I 307, 312, 313 CN-FEM(C) scheme I 356, 357 CN-FEM(G) scheme I 357 CN-MO scheme - and 10 Burgers' equation I 343, 347, 348
Subject Index 475
- and 10 transport equation I 307, 309, 313-315
CN-4PU scheme - and 10 Burgers' equation I 346-348 - and 10 transport equation I 307,
312-315 Cole-Hopf transformation I 333, 361 collocation - orthogonal I 95, 100, 156 - spectral (pseudospectral) method I 151,
154 - (weighted residual) method I 100, 103,
104 compatibility condition (method of
characteristics) I 100, 103, 104 compressible boundary layer flow II 37, 38 - boundary conditions II 37 compressible flow I 7, 13, 16-18, 107,
353-355; II 32-40 - inviscid I 353-355; II 32-36,147-199 - potential, governing equation II 33 - 35 compressible viscous flow II 38-41,
399-452 - boundary conditions II 39-41 - and boundary conditions for Euler
equations II 40, 41 - physical simplifications II 400-403 computational efficiency - Euler vs potential flow codes II 198 - and operation count estimates I 92-94 computer - architecture I 5 - hardware I 4 - speed I 4-7 conformal coordinates II 54 - metrics II 313 conformal mapping - one-step II 93 - 96 - and potential flow II 90 - sequential, for streamlined bodies
II 90-92 conjugate gradient method I 200; II 349 - as an acceleration technique I 201 - 203 connectivity I 358 - 359 conservation - of energy I 11 - of mass I 11, 38, 107 - of momentum I 11 conservation form of Burgers' equation
I 333 consistency I 73, 75 -79 - connection with truncation error I 77 - 78 - of DuFort-Frankel scheme I 220, 221 - of FfCS scheme I 77 - 78 - of fully implicit scheme I 78 - and modified equation method I 290
476 Subject Index
constant total enthalpy condition II 400, 406-408
continuity equation I 34, 105; II 6 continuum hypothesis II 1 contravariant velocity components II 191,
432 convection I 11, 12, 276 convection diffusion equation I 293 - 298 - and cell Reynolds number I 294-296 - and nonuniform grid accuracy I 349-350 - and oscillatory solution I 294 - 295 convection equation, linear I 31, 277 - 286 - algebraic schemes for I 278-279 - numerical algorithms for I 277 - 283 - sine wave propagation I 284-286 convective nonlinearity I 331 - cubic I 359 - quadratic I 359 convective term, asymmetric discretisation
I 276 convergence I 57, 73 -76 - Newton's method I 165, 170, 176 - numerical I 58,60,75-76, 116, 134,226,
235, 236, 239, 240 numerical, for 2D Burgers' equation I 359, 360 pseudotransient Newton's method I 210 quadratic, for Newton's method I 165, 170
- radius of I 166, 179 rate I 76, 78, 116, 134, 226, 235, 236, 239, 240
- rate, numerical I 235, 236, 239, 240 - rate of iteration and strong ellipticity
I 198 coordinate system, element based I 121, 124,
127 - generalised I 352 coordinate transformation I 22-23 correction storage (CS) method (see multigrid
method) I 206 cost of software and hardware I 3 - 6 COUNT. program to obtain basic operation
execution time I 375 Courant (CFL) number I 278 - for compressible flow II 415, 423 - and pseudotransient formulation II 423 CPSM method, boundary conditions for
pressure II 351 - time step restriction II 352 Crank-Nicolson scheme
and four-point upwind scheme I 305 generalised for lD Burgers' equation I 338, 339 generalised for 2D diffusion scheme I 261
- for linear convection equation I 283, 284, 286, 291
- and mass operator method I 305 - and Richardson extrapolation I 90 - for systems of equations I 353 - 355 - for lD Burgers' equation I 337, 338
for 1D diffusion scheme I 228 - 229 - for lD transport equation I 304-305
for 3D boundary layer flow II 242 cross-stream diffusion I 317,326-327;
II 371 curved pipe flow II 296 curved rectangular duct flow II 289 - 296 - computational algorithm II 293 - 294 - vorticity boundary condition
II 293-294 cycle time, computer I 4, 5 cyclic reduction for Poisson equation I 190,
191 cylinder plate junction flow II 359
Davis coupled scheme, for compressible boundary layer flow II 218-221
deferred correction method I 95 degenerate system of partial differential
equations I 26, 27 design and CFD I 1, 2, 5 D!FEX: explicit schemes applied to diffusion
equation I 222-227,236 DIFF: elementary finite difference program
I 66-68 difference operators I 376 - 379 - directional I 377; II 382 diffusion equation, one dimensional (ID)
I 34,40,65,135,146-149,216-241 - algebraic schemes for I 219
explicit methods for I 217 - 222, 226 - implicit methods for I 227 - 23 1
separation of variables solution I 67 diffusion equation, two dimensional (2D)
I 249-251 - and AD! method I 252-253 - and approximate factorisation method
I 254-256 - explicit methods for I 250 - generalised implicit scheme I 254 - implicit methods for I 251 - splitting methods for I 251- 259 diffusion, numerical I 281, 285 diffusion, physical I 11, 12 D!FIM: implicit schemes applied to the
diffusion scheme I 231 - 236 dilatation II 6 direct Poisson solvers I 190-192 direct solution methods for linear algebraic
systems I 164, 180-182
Dirichlet boundary conditions I 20, 36, 37, 108
discretisation I 15, 47 - 60, 136 - accuracy I 55-64 - accuracy for first derivatives I 56 - 58
accuracy via Fourier analysis I 62 - 64 - accuracy for second derivatives I 56- 58
accuracy and truncation error I 56-58 - of derivatives by general technique
I 53-55 of derivatives by Thylor series expansion I 52-53
- grid coarseness I 6 I - higher-order formulae I 58-60,63-64 - nonuniform grid II 278
and ordinary differential equation connection I 51
- and solution smoothness I 58-60 - of spatial derivatives I 49
on a staggered grid II 335 - 337 - of time derivatives I 50- 5 I
and wave representation I 61 -64 discriminant I 22, 23, 25 dispersion, numerical I 286-292 - and Fourier analysis I 288 - 290, 3 I 4, 3 I 5
of a plane wave I 287 and truncation error I 297, 298, 300, 305 and 2D transport equation I 3 I 7
dispersion wake I 286 displacement thickness II 21 -23 - and injection velocity II 3 I 8 dissipation - artificial I 34 I, 348
function II 1 1 numerical I 286-292
- physical I 31, 43, 59 - of a plane wave I 287
and truncation error I 298, 300, 304-306 and 2D transport equation I 326
divergence form of the governing equations I 333
DOROD: prediction of turbulent boundary layer flow II 227 - 237
Dorodnitsyn finite element method II 223-226
Dorodnitsyn spectral method II 237 - 239 - choice of weight functions II 238 Dorodnitsyn transformation, boundary layer
equations II 221 -222 Douglas Gunn splitting algorithm I 255 driven cavity flow II 348, 349, 352, 367, 374,
376, 378 duct flow II 283 - 295 - curved, rectangular II 289-296 - different regimes II 273 - global mass conservation II 275
Subject Index 477
- straight rectangular II 283 - 289 DUCT: viscous flow in a rectangular duct
I 137-143,194-195 DuFort-Frankel scheme I 220-221,226, 301,
302 dynamic similarity II 12-14
eddy viscosity II 24, 277 - Baldwin, Lomax formulation II 404-406,
420 Clauser formulation II 24, 404
- compressible flow II 402 - intermittency factor II 404 - separated flow region II 425 - upstream relaxation II 404 efficiency, computational (see computational
efficiency) I 58 eigenvalue I 23, 81, 83, 84, 245 - annihilation and conjugate gradient method
I 201 - of flux Jacobians II 163- 164, 418, 429 - maximum, and the power method I 84 - and oscillatory solution I 294, 295 element-based coordinates I 378 elliptic partial differential equation I 17, 18,
21-23, 25-27, 29, 36-38, 42-46 - boundary and integral conditions for I 38 energy equation II 10- I I - algebraic (see also constant total enthalpy
condition) II 1 - algebraic, inviscid compressible flow II 33 - algebraic, inviscid compressible flow, ideal
gas II 33 energy method of stability analysis (reference)
I 94 enthalpy II 11 equation coupling and speed of convergence
II 221 ERFC: complementary error function
evaluation I 344 error growth and stability I 79, 81, 85, 86 error of solution I 74, 89, 90, 92, 94, 102,
104, 121, 130, 134, 143 and convection diffusion equation I 298 and linear convection equation I 285 - 286 and mixed Dirichlet/Neumann boundary condition I 268
- and Neumann boundary conditions I 239, 240
- and lD Burgers' equation I 346, 347 - and 10 diffusion equation I 226, 235,
236 and 10 transport equation I 312, 313 and 2D Burgers' equation I 371, 372
- and 2D diffusion equation I 266 and 2D transport equation I 326
478 Subject Index
Euler discretisation scheme I 51, 152, 242 - stability restriction I 245 Euler equations I 8, 353; II 8, 147 -185 - boundary conditions II 178 - 179 - boundary conditions, pseudotransient
form II 180 characteristic form II 170, 448
- factored form of scalar tridiagional system II 177
- generalised "viscous" boundary condition II 326
- implicit schemes II 174-181 - multigrid algorithms II 181-185 - one dimensional II 151 EXBUR: exact solution of 2D Burgers'
equation I 175 execution time for basic operations I 375 explicit schemes
for compressible Navier-Stokes equations II 410
- for ID Burgers' equation I 334-337, 346-347
- for 10 diffusion equation I 217 - 227 for 10 transport equation I 299 - 303 for 2D diffusion equation I 250-251
- for 2D transport equation I 316-317 EXSH: exact solution of ID Burgers' equation
I 344 EXSOL: exact solution of ID transport
equation I 311 EXTRA: exact solution of 1 D diffusion
equation I 222, 225 EX-4PU scheme for 1 D transport equation
I 307
FACR algorithm I 191 factorisation, approximate (see approximate
factorisation) I 254 FACT/ SOLVE: solution of dense systems of
algebraic equations I 180-182 fast Fourier transform I 153, 156 FCI: propagating shock wave by FCT
algorithm II 171-174 finite difference discretisation I 47 - 53,
56-60 finite difference method I 13-15,64-69,92,
95, 100, 143 - and matrix structure I 163 finite difference operators I 138, 228, 230,
250, 270, 279, 303, 335 finite element method I 15, 116-145,
256-266 - and bilinear interpolation I 121-122, 125 - and biquadratic interpolation I 123 - 126
and compressible Navier-Stokes equations II 425-426,438-442
- and diffusion equation I 135 -136 - and discretisation I 48-50, 129, 136, 139 - Dorodnitsyn II 223 - 237 - Euler equations II 200 - in generalised coordinates II 439-442 - and incompressible Navier-Stokes equations
II 368-373, 382-390 - and interpolation I 116 - and linear interpolation I 117 - 119 - nonoscillatory II 371 - and Poisson equation I 137 - 138 - and quadratic interpolation I 119 -121 - and Sturm-Liouville equation I 126-135 - and transonic potential equation II 198 finite elements I 121-123, 126 finite volume method I 15, 105 -116
accuracy and grid refinement I 116 - and compressible Navier-Stokes equations
II 420,452 and discretisation I 48 and Euler equations II 182-185,200
- and first derivatives I 105 -107 - and general-purpose code,
RANSTAD II 362 - and incompressible Navier-Stokes equations
II 362-363 iterative convergence and grid refinement I 116
- and Laplace's equation I 111 -116 - and second derivatives I 107 -111
and transonic potential equation II 198 first derivative operator and Galerkin weighted
integral I 378 FIVOL: finite volume method applied to
Laplace's equation I 111-115 flat plate solar collector I 166, 167 flow classification II 14 - 16 flow separation I 8 flux, antidiffusive II 165 -166 flux difference splitting II 164, 304 flux Jacobians II 163,175,178,182,418,
422, 429, 448 and artificial compressibility method II 357 -358
- for compressible RNS formulation II 300 - eigenvalues II 429 - in generalised coordinates II 433
for positive and negative eigenvalues II 163 -164
flux limiters, antidiffusive II 168, 448 flux vector splitting II 164, 304, 360, 438 - and TVD schemes II 451 flux vectors, in generalised coordinates II 433 flux-corrected transport schemes II 164 - 166 - dispersion error minimisation II 166 - stability restriction II 166
- TVD interpretation II 168 flux-limiting scheme, and numerical dissipation
II 449 four point upwind scheme (see upwind
scheme) I 296-298 Fourier (stability) analysis I 80, 85 - 88 - for linear convection equation I 288 - 290 - for 10 transport equation I 310, 314 - 315 Fourier analysis, pde classification I 28 - 30 Fourier representation of wave-like motion
I 61, 62 Fourier series as approximating and weight
functions I 146 Fourier series method for Poisson equation
I 190, 191 Fourier transform and symbol of pde I 29 Fourier's law II 4 fractional step method II 348 frontal method and sparse Gauss elimination
II 369 Froude number II 12-14 FTCS scheme I 65, 156, 217 - 220, 226, 236,
239 - and Burgers' equation I 334, 346 - and Euler schemes I 243 - fourth-order accuracy I 77 - and linear convection equation I 277, 278 - and Richardson extrapolation I 91 - stability of I 81- 82, 85 - 86 - and 2D diffusion equation I 250 fully implicit scheme for diffusion equation
I 227-228
Galerkin finite element method I 126-144, 355-359
- boundary implementation I 269 - incompressible Navier-Stokes equation
II 368-370 Galerkin spectral method I 147, 150 Galerkin (weighted residual) method
I 101-104, 377 Gauss elimination I 152, 180 -183 - narrowly banded I 184-186 - sparse I 182-183 Gauss quadrature I 145; II 372 Gauss-Seidel iterative method I 193 -196 general three-level scheme for lD diffusion
equation I 229, 230 - for 2D diffusion equation I 255 generalised coordinates I 22, 43, 107, 156;
II 47-77 - for compressible RNS equations II 298,
299 and compressible viscous flow II 430-441 equation structure II 64 - 69
Subject Index 479
- equation structure for compressible momentum equation II 68 equation structure for continuity equation II 67
- equation structure for first-order pde II 64-66
- equation structure for incompressible momentum equation II 67 - 68
- equation structure for second-order pde II 65-66
- and Steger thin layer formulation II 431 - and 3D boundary layer flow II 243 - 244 global constraint and elliptic partial differential
equation I 38 global method vs local method I 14, 15, 145,
156 governing equations for fluid flow II 5 -11 Green's function method I 41-42 Green's theorem I 38 grid control, source terms in Poisson equation
solver II 103 grid generation I 7, 8; II 81-123 - algebraic mapping II 104-123
boundary correspondence II 83 - 89 boundary correspondence, multiplyconnected regions II 86-89 boundary correspondence, simply-connected regions II 83 - 85 as a boundary value problem II 81, 82 conformal mapping II 89 - 96 partial differential equation solution II 89-104
- Poisson equation solution II 100-103, 124
- unstructured (references) II 125, 185 grid growth ratio I 349, 377; II 279 grid non uniformity and solution accuracy
I 348-352 - and truncation error I 349, 350 grid point clustering, 1-D boundary stretching
II 105-106 grid refinement
and accuracy I 58-61, 75, 89-92, 119, 121,134,143,226,235-240,266
- and iterative convergence I 192, 195, 198; II 76
group finite element method I 355 - 360 - approximate factorisation II 424-425 - comparison with conventional finite element
method I 358-360 - compressible Navier-Stokes equations
II 423-426 - computational efficiency I 356
inflow and outflow boundary condition II 385 - 386 one-dimensional formulation I 356
480 Subject Index
group finite element method (cont.) operation count for I 358 - 359
- two-dimensional formulation I 357 - 358 - vorticity stream function formulation
II 382-386 - and lD Burgers' equation I 340
and 2D transport equation I 319 - 320
heat conduction equation I 34, 48, 64 - 66, 135,216-217
higher order difference formulae I 58 - 60, 63-64
higher order explicit schemes for diffusion equation I 221, 226
higher order implicit schemes for diffusion equation I 230, 231
hopscotch method I 251 hydrostatic pressure II 2 hyperbolic partial differential equation
I 17-19,21-23,25-27,30-38,43-45 boundary conditions for I 32-34 characteristics for I 30 - 31 and discontinuity propagation I 89 domains of dependence and influence I 31
- initial conditions for I 31
ideal gas equation II 2 ill-conditioned system of equations I 186 implicit schemes
for compressible Navier-Stokes equations II 415-430
- for diffusion equation I 228 - 236 - for the lD Burgers' equation I 337 - 339 - for the lD transport equation I 304-306 implicitness parameter I 82, 87, 136 inclined cone problem, inviscid compressible
flow II 158 - MacCormack two-stage algorithm II 159 inclined hemisphere cylinder, compressible
viscous flow II 437 -438 incompressible Navier-Stokes equations,
boundary conditions II 26-28, 336 incompressible viscous flow II 26-32,
II 337-373 turbulent II 30 - 32 vorticity formulations II 373 - 396
incompressible, inviscid flow II 16 - 20 initial conditions I 19, 20, 241 instability, nonlinear I 154 - physical I 88 integral boundary condition for the
pressure II 340
integral form, governing equation I 106 internal swirling flow II 277 - 283 - marching iterative algorithm II 278 - 282 interpolation I 116 - 126 - bilinear I 121-122, 125, 144; II 370, 382,
424,439 - biquadratic I 123 -125; II 370
error I 119, 121, 125 function I 118,120,121-123,377 higher-order I 121, 126, 134 linear I 117 -119, 134 mixed velocity, pressure II 370 multigrid I 204-207 quadratic I 119-121, 134
inviscid Burgers' equation I 332, 333, 335, 337
inviscid, compressible flow II 32 - 36, 147-200
inviscid flow I 7 - 8, 13, 16, 18 - 20, 30, 32-33,44-45,59, 116,353-355; II 128-200
- alternative equation systems II 128 isoparametric formulation I 143 -145 iterative methods for algebraic systems of
equations I 192-207 - convergence acceleration I 200 - 207 - convergence acceleration via iterative
sequence I 197, 214, 215 - convergence rate and grid refinement
I 198; II 76 - convergence rate and strong ellipticity
I 198 - Gauss-Seidel method I 193 - general structure I 192
implicit algorithms I 196 - 200 Jacobi method I 193
- point vs line methods I 195 - SLOR method I 197 - SOR method I 193
JACBU: evaluates Jacobian of 2D Burgers' equations I 177, 211
JACOB: evaluates Jacobian required by Newton's method I 169, 170
Jacobi iterative method I 193 - 197 - and pseudotransient method I 208 Jacobian
augmented I 210 - flux (see flux Jacobian) - Newton I 165,169,170,172,211,212 - transformation I 23, 145; II 48
Keller box scheme II 214 Khosla-Rubin differencing II 376-377 Klebanoff intermittency factor II 405 Korteweg-de Vries equation I 44
LAGEN: solution of Laplace equation in generalised coordinates II 69-77
Lagrange interpolation function I 120, 123, 124,126
LAMBL: computation of laminar boundary layer flow II 207 - 214
Laplace's equation I 13,107-116 - in conformal coordinates II 54 - discretisation in generalised coordinates
II 70-72 in generalised coordinates II 54, 69
- in orthogonal coordinates II 54 Lax equivalence theorem I 74 Lax-Wendroff scheme
and linear convection equation I 281-283,291-292 and systems of equations I 353 - 355
- two-stage I 335, 336, 346, 353 - 354 - and to transport equation I 301, 303,
307, 312 leapfrog scheme for linear convection equation
I 281, 282 least-squares (weighted residual) method
I 100, 103 Leith's scheme I 282 Levy-Lees transformation, compressible
boundary layer flow II 216-218 locally one-dimensional method (see method
of fractional steps) I 272 LU factorisation (approximate) algorithm
II 430 - for compressible Navier-Stokes equations
II 427 -431 - and one-sided operators II 427 LU factorisation and Gauss elimination I 169 LU-factorisation, incomplete I 207
MAC formulation II 337-341 boundary condition implementation II 340, 341
- explicit schemes II 337 - explicit schemes, stability restriction II 339
in generalised coordinates II 344 - 345 - implicit schemes II 342
Neumann boundary condition for pressure II 342
- pressure correction method II 344 - and satisfaction of continuity II 339 MacCormack scheme, explicit I 354;
II 148- 151 inclined cone problem II 158
- and Lerat-Peyret schemes II 149 - and multigrid method II 413 - for Navier-Stokes equation II 411 - time-split extension II 412-413 - time-step restriction II 412, 413
Subject Index 481
- for 2D Burgers' equation II 410 MacCormack scheme, implicit
bidiagonal implementation II 417 for compressible Navier-Stokes equation II 417-419
- stability restriction II 416 - for lD transport equation II 415-417 Mach lines II 35 Mach number I 18; II 13-14 MACSYMA, symbolic manipulation I 291 mass conservation for enclosures, global
II 334 mass conservation for steady duct flow,
global II 275 mass flow constraint and mean pressure
evaluation II 276, 280 mass lumping, and computational efficiency
II 388 mass operator
and bilinear interpolation I 256 - boundary evaluation I 270-271;
II 385-386 - computational scheme I 307, 338, 362,
376-379 - directional I 136, 138, 139, 377;
II 382, 425, 440 and Galerkin weighted integral I 378
- generalised, and dispersion I 305, 345 - and linear interpolation and fourth-order
accuracy I 379 - and Pade differencing I 379 - and three dimensional discretisation I 379 mass-weighted Reynolds averaging II 401 matrix - banded I 163
dense I 163 diagonal dominance I 192 fill-in I 182 positive definite I 179
- sparse I 163, 182 spectral radius I 192
- structure for finite difference scheme I 163
maximum principle for elliptic partial differential equations I 37
megaflop I 4, 6 method of characteristics I 38 - 40 method of fractional steps I 271-273 method of lines and ordinary differential
equations I 241-246 metric tensor II 51, 52 - and conformal coordinates II 54 - and grid aspect ratio II 52 - and orthogonality II 52 - 54
482 Subject Index
metric tensor (cont.) - and transformation Jacobian II 52 microcomputers and CFD I 6 minicomputers and CFD I 6 mixed velocity, pressure interpolation
(FEM) II 370 mixing length, turbulent II 24 modified equation method I 290-291 - and 1D transport equation I 305, 306 - and 2D transport equation I 324 momentum equations - factored form for spatial marching II 285,
286 - for inviscid flow II 6 - 8 - for viscous flow II 8 - 10 monotone schemes for shock prediction
II 167-168 Moretti scheme II 161-163 - logarithm of pressure II 161 - non-conservative form II 163 - role of characteristics II 161-163 multigrid method I 203 - 207, 211
and auxiliary potential function II 362 - correction storage (CS) for linear problems
I 206 driven cavity flow problem II 378 and Euler equations II 181 - 184 full (FMG) I 207
- full approximate storage (FAS) for nonlinear problems I 207; II 438
- and incompressible RNS equations II 316 and MacCormack scheme (explicit) II 413 Ni control volume formulation II 181-184 and prolongation (interpolation) operator I 204 and restriction operator I 204 - 205 and Runge-Kutta schemes II 415 and transonic potential equation II 195-197 and V-cycle I 205
multistep-method, linear, for ordinary differential equations I 242
multisurface technique effect of control parameters II 123
- implementation, N = 2 II 116-119 - and local grid orthogonality II 110, 112 multisurface transformation II 110
Navier-Stokes equations I 1, 19-20,28, 35, 37, 43; II 9-10
- reduced form I 1, 8, 28; II 252 - 327 - thin layer form I 8 Neumann boundary conditions I 20, 36-38,
236-241; II 339, 340 - and accuracy I 133, 238-240, 268
- finite difference implementation I 267-268 finite element implementation I 269-271
- and finite volume method I 1 1 1 - numerical implementation I 237 - 238
and spectral method I 149 and splitting I 266 - 271
- and stability I 83 - 85 NEWTBU, inclusion of augmented Jacobian
I 210-211 NEWTBU: two dimensional Burgers'
equation I 171-179 NEWTON: flat plate collector analysis
I 166-170 Newtonian fluids II 4 Newton'smethod 1163-166
and finite element method II 369 and incompressible RNS equations II 315
- and Keller box scheme II 215 and mean pressure evaluation II 285
Ni's control volume multigrid method II 182-183
nondimensionalisation I 12, 137; II 12-13, 152
numerical dissipation II 358, 359, 424, 435, 442-445
- and aliasing II 444 - approximate factorisation II 445 - and dispersion I 287 - 293
dispersion and discretisation schemes I 292
- dispersion and Fourier analysis I 288 - 290 - and flux-limiting schemes II 444 - fourth-order II 445, 446
and high Reynolds number flows II 301 , 445-446 and modified density function II 191 and modified equation method I 290-291 and pressure oscillations II 445 stability restrictions II 158 and TVD schemes II 449
O-grid and branch cuts II 86-87 one-sided differencing I 50, 54 operation count
and block Thomas algorithm I 189 - empirical determination I 92 - 94 - and finite element method I 358, 359 optimal-rms solution and weighted residual
method I 103 ordinary differential equations I 241 - 246 - and absolute stability I 244 - and linear multistep methods I 242 - 243 - and Runge-Kutta schemes I 243-245 orthogonal collocation I 95, 100, 156 orthogonal function I 146, 147
orthogonal grid generation II 97 - 99 via elliptic partial differential equation II 104 via orthogonal trajectory method II 98, 99
orthogonal trajectory method as a method of characteristics II 99
orthogonality of coordinates II 52- 54 - discrete II 56, 57 ORTHOMIN algorithm I 202 orthonormal functions II 237, 238 oscillatory pressure solutions II 336 - and finite element interpolation II 370
panel method I 182; II 129 - 146 - connection with boundary element method
II 141-142 higher-order II 144- 145 for inviscid compressible flow Ii 146 for inviscid incompressible flow II 130- 145
- and lifting aerofoil problem II 142- 144 - in three dimensions II 145 PANEL: numerical implementation of panel
method II 134- 140 panel source strength, circulation adjustment
II 142-144 parabolic partial differential equation I 17,
18,21-23,25-26,34-38 - boundary conditions for I 36 parallel processing I 5 - 6, 16 - and explicit algorithms II 452 partial differential equations (pde) I 17-42 - boundary and initial conditions for
I 18-20 - classification by characteristics I 17,
21-24 - classification by symbol (Fourier)
analysis I 28 - 30 and coordinate transformation I 22-23
- first-order I 2 I, 24 - linear I 12 - principal part I 28 - second order I 17, 21 - and symbol I 29 - system of equations I 24-28 Peclet number I 294, 305 penalty function finite element method
II 371 -373 - consistent II 372-373 - for incompressible viscous flow
II 371-373 - and pressure smoothing II 373 - and reduced integration II 372 pentadiagonal systems of equations/ matrix
I 131,185-188
Subject Index 483
Petrov-Galerkin finite element method and upwind differencing II 371
phase, change of I 289 phase error I 63 physical properties
of air II 2-5 of fluids II 1-5
- of fluids, variation with temperature II 3-5
- of water II 2-5 pipe flow, different flow regimes II 273 pipeline architecture I 4- 5 pivoting, partial and Gauss elimination 180 planar shock traverse past an aero foil
II 449-450 plane-wave propagation I 287 point source I 41 Poisson equation I 37-38,41-42,137 - for auxiliary potential II 286, 36 I - for grid generation II 100- 103 - for pressure II 365, 391 - for pressure, discrete II 339, 365 - for pressure, global integral constraint
II 391 - for stream function II 374 - for transverse pressure correction II 287 Poisson solvers, direct I 190- 192 potential flow I 36
about a circular cylinder II 25 compressible II 33 governing equation II 17
- incompressible II t7 - 20, 129 power method for maximum eigenvalue
determination I 84 PrandtI number I 319; II 13 - 14 PrandtI-Glauert transformation II 146 preconditioned conjugate gradient method
I 201 -203 predictor corrector scheme for ordinary
differential equations I 243 pressure evaluation (mean) from mass flow
constraint II 276, 280 pressure solution from Bernoulli variable
II 391 -392 pressure splitting in small-curvature ducts
II 275, 284 primitive variables I 34 product approximation I 360 projection method II 343, 350 prolongation operator (see also multigrid
method) I 204-206 pseudospectral method I 151 -154; II 349 - in physical space I 154 - 156 pseudotransient method I 8, 208-212 - and artificial compressibility method
II 356
484 Subject Index
pseudotransient method (cont.) comparison with Jacobi iteration I 212
- local timestep formulae II 181 - and Newton's method I 214 - and 20 steady Burgers' equation I 213
quadridiagonal matrix I 297, 338 - and the Thomas algorithm I 297, 306 quasi-Newton method I 179 quasi-simultaneous method (see viscous
inviscid interaction) - and triple deck theory II 322 QUICK upwind scheme II 346, 349, 368 QUICKEST upwind scheme II 347-349
Rankine-Hugoniot shock relations II 35, 36, 152, 186
rational Runge-Kutta (RRK) scheme II 413, 414
reduced Navier-Stokes (RNS) equations II 252-326
RESBU: evaluates residuals of 20 Burgers' equations I 176
RESID: evaluates residuals required by Newton's method I 169
residual averaging II 413 residual, equation I 99- 104, 127, 146, 176 - evaluation for finite element method
I 261, 266 and multigrid method I 203 - 207
restriction operator (see also multigrid method) I 204
Reynolds number I 2, 8, 27, 59, 294, 305, 319,325,339,369; II 12-14
equations II 401 - boundary conditions for II 403-406 RHSBU: evaluates right-hand side of 20
Burgers' equations I 370 Richardson extrapolation I 89-92, 241
active I 91 - and operation count I 91 -92 - passive I 91 Richardson scheme I 220 RNS approximation in generalised coordinates
II 299 RNS convection diffusion operator, parabolic
nature II 262,264-265 RNS equations
defect representation II 323 and the design process II 253 - 254 and dominant flow direction II 255
- essential features II 255 - and finite element method II 329
- (incompressible) in conformal coordinates II 313
- (incompressible) one-sided discretisation II 314
- for internal flows II 273 - 295 - and neglect of streamwise diffusion II 255 - order-of-magnitude derivation II 256-260
qualitative solution behaviour II 263 - 267 role of pressure II 265, 267 subsonic computational algorithm II 308-311
RNS formulation elliptic viscous terms II 266, 267, 301 for external flow II 296- 326
- for external supersonic flow II 297 - 302 - for incompressible viscous flow
II 311-317 - iterative solution II 301
turbulent flow II 329 RNS marching stepsize restriction - and iterative convergence rate II 315 - and stability II 301, 304, 308 RNS sublayer approximation to pressure
II 297-299 Robin boundary condition I 20 round-off error I 74, 79, 80, 86 Runge-Kutta method I 242-245 - explicit I 242, 244 - implicit I 243 - and multigrid method II 415
for Navier-Stokes equation II 413 - for Navier-Stokes equation, time-step
restriction II 414
Schwartz-Christoffel transformation applied to two-dimensional duct II 94 - 95
- for continuous surfaces II 96 - for discrete surfaces II 93 search direction and modified Newton's
method I 176 secondary flows induced in curved ducts
II 274 semi-discrete form of partial differential
equations I 242 semi-inverse method II 323 - 325 - boundary conditions II 323, 324 separation of variables method I 40-41 Serendipity elements I 126 shape (interpolation) functions I 117 shock capturing, theoretical considerations
II 167 shock fitting II 148 shock formation I 332 shock profile - and artificial viscosity II 158 - and dispersion errors II 153
- Fourier decomposition II 443 - and TVD schemes II 168 SHOCK: propagating shock wave problem
II 151-157 shock propagation speed II 153 shock wave I 7, 32, 43
compression vs expansion II 187 propagation I 353-355
- propagation and Burgers' equation I 339, 346-348, 357
- representation and conservation form of equations II 148
- in generalised coordinates II 368 - incompressible viscous flow II 362- 367
and multigrid II 368 pressure solution II 365 pressure solution, and auxiliary potential function II 365 and QUICK differencing II 368 velocity solution II 364- 365
SIMPLEC algorithm, incompressible viscous flow II 366, 367
SIMPLER algorithm, incompressible viscous flow II 366, 367
skin friction coefficient II 21, 23 - discrete evaluation II 213 - for flow past a wedge II 214 smoothness of solution and accuracy of
representation I 58, 60, 61, 236 sound speed II 33 source panels, connection with an isolated
source II 130 specific heat II 11 spectral method I 11, 15, 16, 47, 48, 50, 98,
99,104,145-156,182 - and Burgers' equation I 348 - and compressible Navier-Stokes equations
II 452 - and diffusion equation I 146-149 - and generalised coordinates II 354-355 - and incompressible Navier-Stokes
equations II 349-354 and Neumann boundary conditions I 149-151
- and nonlinear terms I 149 in physical space I 154 and shock waves II 198, 200 time-stepping strategies for II 353
Subject Index 485
- and transition phenomena II 354 spectral subdomain method II 354-355 - and inter-element continuity II 355 splitting (see approximate factorisation) stability I 15,55,73-75,79-88 - absolute, for ordinary differential equations
1244 - of ADI scheme I 253 - at boundaries I 88, 238 - of convection equation schemes I 278, 279 - of diffusion equation schemes I 219
matrix method and FTCS scheme I 81 - matrix method and generalised two-level
scheme I 82 - matrix method and Neumann boundary
conditions I 83 - 85 - polynomial for ordinary differential
equations I 244 - of three-level scheme for 1 D diffusion
scheme I 222 of transport equation schemes I 302, 303
- von Neumann method and FTCS scheme I 85 -86 von Neumann method and generalised two-level scheme I 86-88
staggered grid II 335-337,362-363 steady flow problems, overall strategy I 211,
212 stiff systems of equations I 229, 246; II 359 - and steady-state convergence I 229, 230 stream function II 28 - 30, 373 stream function equation, pseudotransient
formulation II 374 stream function, Poisson equation for II 373 streamline diffusion (artificial) I 327 streamlines II 16 streamwise diffusion, neglect of II 277 streamwise vorticity in a curved duct II 290 stretching function, one dimensional
II 105-106 strong shock computation II 164-170 strongly implicit procedure (SIP) I 198 -199 - and incompressible viscous flow II 376 - modified (MSI) algorithm I 199-200 STURM: computation of the Sturm-Liouville
equation I 130-134 Sturm-Liouville equation I 126-135 subdomain method I 100, 103, 105, 106, 108 successive over-relaxation (SOR) iterative
method I 111,139,193-198 supercomputer I 2 supersonic flow I 7 - 8, 18, 30, 58 - inviscid flow II 147 -184 - past a blunt fin on a plate II 420, 421 surface pressure evaluation via I D integration
II 391
486 Subject Index
switching formulae, sonic line and shock location II 188
symbolic (Fourier) analysis - and characteristic analysis II 263 - of compressible RNS equations
II 266-267 - of constant enthalpy compressible RNS
equations II 265 - 266 - of incompressible RNS equations
II 263-264 - of 2D transport equation II 260-263 symmetric SOR (SSOR) iterative method
I 194 system of algebraic equations I 163 -164 - nonlinear I 164 system of governing equations I 24-28, 331,
353-355
tau method I 151 Taylor series expansion I 52 Taylor weak statement (TWS) of finite element
method I 292; II 371 Taylor-Galerkin finite element method I 292 temperature I 3, 11, 12, 48, 64, 166, 277,
305, 318 temperature front convection I 305 - 306,
312, 313 tensor product I 138, 139, 256, 377 term-by-term finite element discretisation
I 136, 139 test function I 100 TEXCL: semi-exact centreline solution I 320,
325 Theodorsen-Garrick transformation II 92 THERM: thermal entry problem I 318-326 thermal conductivity II 3-5 thermal diffusivity I 48, 82 thermal entry problem, centre-line solution
II 272, 273 thin layer approximation II 299, 400,
408-409 - for adjacent surfaces II 409 - and RNS equations II 409 thin shear layer flows II 26 Thomas algorithm I 130, 136, 183 - 184 - block I 188-189 - generalised I 187 - 188 - and line iteration method I 194 THRED: thermal entry problem via single
march solution II 267 - 273 three level explicit scheme I 221, 226 three level fully implicit scheme I 227 three level generalised implicit scheme
I 229 total energy per unit volume II 40 total enthalpy II 406
total variation diminishing (TVD) requirement II 168
trajectory method for near-orthogonal grids II 99, 100
TRAN: convection of a temperature front I 305-316
transfinite interpolation I 8; II 112-114 - and grid orthogonality II 114 transformation parameters (metrics) II 50 - evaluation via centred differences II 56,
57 - evaluation via finite element formulation
II 57, 58 - evaluation via finite volume formulation
II 59, 60 - inverse II 50 transformation relationships II 49- 54 transonic, inviscid flow II 185 - 198 transonic potential equation II 186, 189 -190 - and finite element method II 198 - and finite volume method II 198 - and generalised coordinates II 191 -192
iterative schemes II 193 -196 multiple solutions II 198 non-isentropic II 197 -198 and Rankine-Hugoniot condition II 186 small disturbance II 187 - 189 small disturbance and jump conditions II 187 switching function II 190
transport equation, one dimensional (1D) I 12, 35, 299-316 algebraic schemes I 302, 303 explicit schemes for I 299-303, 312 implicit schemes for I 304-306, 312, 313 phase behaviour of discrete schemes I 310, 314, 315
- separation of variables solution of I 306 transport equation, two dimensional (2D)
I 316-328, 376-377; II 268 - split formulations for I 317-318 transverse pressure correction - boundary conditions for II 287 - in duct flow II 284, 287 - Poisson equation for II 287 transverse velocity splitting II 289 - 292 - irrotational components II 290, 291 - order-of-magnitude analysis II 291 - rotational components II 290, 291 - symbolic analysis of II 292-293 trapezoidal scheme for ordinary differential
equations I 243 trial function I 98-101 - and finite element method I 117 trial solution and finite element method
I 127, 137
triangular elements I 143 tridiagonal systems of algebraic equations
I 136, 183-184,252 truncation error I 49, 52 - 57, 61
cancellation I 77, 90, 221, 226, 231 - and consistency I 76-79
and dissipation and dispersion I 290-291 - in generalised coordinate formulae
II 60-63 - leading term I 56, 57 turbulence
direct solution I 149 - dissipation rate II 32, 33
kinetic energy II 32, 33, 403 (mixing) length scale II 405
- modelling, algebraic eddy viscosity formulae II 24, 405
- modelling, compressible flow II 402 - 403 modelling, k-e II 32-33 Prandtl number II 403 wall functions II 33, 407
TVD property II 168, 413 TVD schemes II 446, 451 - as added numerical dissipation II 449 - in generalised coordinates II 449
implicit II 447 - 449 - one-step nature II 169
stability restriction II 447 for systems of equations II 170 for 1D Euler equations II 448-449
TWBURG: 2D Burgers' equation numerical solution I 364-372
TWDIF: generalised FD/FE implementation I 259-266
two-boundary technique and local grid orthogonality II t 07
upwind differencing, supersonic regions II 178
upwind scheme, four point I 296-298; II 296
- accuracy of I 298, 312, 313 - for incompressible viscous flow
II 345-348 and qopt I 345
- QUICK scheme II 346, 349, 367 QUICKEST scheme II 347 - 349 and suppression of dispersion I 298
- and ID transport equation I 305, 306; II 346 and 1D Burgers' equation I 335, 338 and 2D transport equation I 324-326
- and 2D Burgers' equation I 364 upwind scheme, two point - and convection diffusion equation I 295,
296
Subject Index 487
- and cross-stream diffusion I 317 - and linear convection equation I 278, 279,
281 - and 1 D transport equation I 301, 302
V-cycle, multigrid I 204 vector potential II 392 - surface boundary conditions for II 393 vector processing I 4, 5, 16 VEL: velocity in channel at specified location
I 142 velocity I 47, 89, 137,277, 319 velocity potential I 13; II 17, 33 Vigneron criterion and stepsize restriction
II 308, 309 Vigneron RNS strategy
for axial pressure gradient adjustment II 301-304
- discrete Fourier analysis II 306, 307 - symbolic analysis II 302- 304 viscosity II 3 - 5 viscous dissipation I 34 viscous flow I 59, 98, 116, 137, 156, 276,
332, 336, 359 viscous, inviscid interaction II 317 - 326 - close to separation II 318 - direct method II 318, 319
inverse method II 318 - quasi-simultaneous method II 320- 322 - semi-inverse method II 319, 320, 323 - 325 - using Euler equations II 326, 327 viscous inviscid region, coupling formulae
II 318-320, 324, 325 viscous stresses II 9 von Karman-Trefftz transformation II 90 von Neumann method of stability analysis
I 85-88 - and convective nonlinearity I 372 vortex methods (reference) II 397 vorticity II 28 - 30 - boundary condition at surface
II 378 - 380, 393 - boundary condition at surface,
pseudotransient implementation II 385 - formulation, in three dimensions
II 392- 395 - singularity at sharp edge II 387 vorticity stream function formulation - boundary conditions II 378 - 381 - finite difference algorithm II 375 - 377 - group finite element method
II 382-386 - and incompressible viscous flow
II 373-392 - integral boundary condition II 374
pressure solution II 390- 392
488 Subject Index
vorticity transport equation, three dimensional II 392
vorticity transport equation, two dimensional II 373
vorticity vector II 373 vorticity, vector potential formulation - and auxiliary potential II 394 - inflow, outflow boundary conditions
II 393 - and satisfaction of continuity II 394 - in three dimensions II 393 - in two dimensions II 393, 394
wave equation I 30 wave number I 61 - cut-off II 444 - representation on a finite grid II 443 wave propagation and dissipation/dispersion
I 287-290
wave propagation speed I 62, 289 wave representation I 60-64 wavelength I 61 - and error distribution I 200 - attenuation and dispersion I 287 - behaviour for lD transport equation
I 314, 315 weak form of governing equation I 100 weather forecasting I 3, 11 wedge boundary layer flow II 208, 214 weight function I 100, 101, 135, 146;
II 370, 372 weighted residual method I 98- tol - and comparison of constituent methods
I tol-105 well-posed problem I 18-20 wind-tunnel experiments vs CFD I 2
zonal method I 8; II 400-401
Contents of
Computational Techniques for Fluid Dynamics 1 Fundamental and General Techniques
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