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| Finlayson B.A. — Numerical Methods for Problems With Moving Fronts |
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| Предметный указатель |
Displacement, immiscible 8
Displacement, immiscible, diagonal grid 533
Displacement, immiscible, Galerkin method 534
Displacement, immiscible, one-dimension 503
Displacement, immiscible, parallel grid 533
Displacement, immiscible, two dimensions 531
Displacement, immiscible, upstream 5-point 534
Displacement, immiscible, upstream 9-point 534
Displacement, miscible 8 500
Displacement, miscible, diagonal grid 528 531
Displacement, miscible, one-dimension 500
Displacement, miscible, parallel grid 529 531
Displacement, miscible, two dimensions 527
Dissinger, G. R. 220 254
Dissipation 4 308
Dissipation, numerical 51 60—67
Divergence 442
Divergence formulation 533
Divergence of dyadic 453
Divergence theorem 265 301 437
Divided difference table 155
Domain, infinite 409
Domain, semi-infinite 403
Domain, transformation 405
Domain, truncate 7
Domain, truncated 302
Donea, J. 97 99 125 322. 449 455
Doss, S. K. 223 234 235 254 383—385 400
Douglas, J., Jr. 240 243 254
Dudukovic, M. P. 396 400
DuFort — Frankel method 70 82
DuFort — Frankel Method, Burger’s equation 70
DuFort — Frankel Method, convective diffusion equation 77 82
DuFort — Frankel Method, filtered 77 82
DuFort — Frankel Method, filtered, truncation error 81
Dukowicz, J. K. 263 315
DuPont, T. 218 233 254
Durlofsky, L. J. 151 152 186 508 540
Dwyer, H. A. 220 254 383 399
Dyadic, fourth order 453
Effectiveness factor 392
Eigenfunction 478
Eigenvalue 480
Eigenvalue, polymer problem 482 483
Eigenvector 477
Eisenstat, S. C 260 315
El-Ageli, M. A. 180 186
Elastic displacement 228
Electro-chemical machining 3
Electronic chips 402 428
Element, first 322
Element, integral 22 471 473
Element, isoparametric 296
Element, last 40 98 104 105 108 321
Element, macro 216 217
Element, matrix 24
Element, micro 216 217
Element, moving 217 218
Element, numbering 146
Element, space-time 245
Element, triangular 266 267
Elongation rate 459
Energy conservation, latent heat device 3
energy equation 435
Engleman, M. 436 456
Engquist, B. 151 152 186 508 540
ENO Method 6 151 155—159
ENO Method, advection equation 159
ENO Method, Buckley — Leverett problem 511 512 585
ENO Method, Burger’s equation 160 583
ENO Method, comparison 158 183 248 249 250
ENO Method, convective diffusion equation 159 582
ENO Method, inflow and outflow 158
ENO Method, rotating cone problem 351
ENO Method, two dimensional 275
Enthalpy method 416—419
Enthalpy method, freezing in comer 424 425
Equation, continuity 461
Equation, elliptic 8 93 499
Equation, elliptic pressure 531
Equation, gas dynamics 129
Equation, homogeneous 463
Equation, hyperbolic 8 55 73 129 151 449 499
Equation, hyperbolic saturation 531
Equation, hyperbolic, linear theory 319
Equation, hyperbolic, real eigenvalues 477
Equation, hyperbolic, semi-linear theory 319
Equation, integro-differential 394
Equation, momentum 460
Equation, parabolic saturation 531
Equation, quasi-linear 333
Equation, semi-linear 479
Equation, telegrapher’s 476
Error see “Truncation error”
Error function 410
Essenhigh, R. H. 397 400
Ettouney.H. M. 430 431
Euler method 30 31 33 45 463
Euler method, comparison 464 468 469
Euler method, initial value problem 453 464 468
Euler method, stability limits 369
Euler — Lagrange Method 238 291
Euler — Lagrange Method, advection equation 243 245
Euler — Lagrange Method, Burger’s equation 243 246
Euler — Lagrange Method, comparison 248 249 250 251 332
Euler — Lagrange Method, convective diffusion equation 244 245
Euler — Lagrange Method, explicit 241
Euler — Lagrange Method, implicit 240
Euler — Lagrange Method, linear adsorption 326 330 332
Ewing, R. E. 240 254
Explicit method 5 6 30 33 36 47 51 213 257
Farmer, C. L. 239 254
Farooq, S. 335 353
Ferguson, N. B. 194 254
Fiber, freeze-coating 402
Fingering 527 538
Fingering, random choice method 539
Finite difference method 3 12—16 45 55—92 397
Finite difference method, 3-point upstream, comparison 173 185
Finite difference method, 3-point upstream, convective diffusion equation 173
Finite difference method, amplification factor 370
Finite difference method, average permeability 519
Finite Difference method, centered 28 35 37 44 45 80 83 84 368
Finite Difference method, centered, advection equation 65
Finite Difference method, centered, Burger’s equation 70 583
Finite Difference method, centered, comparison 87 95 173 178 185 464 468 488 503
Finite Difference method, centered, convective diffusion equation 36—39 77 80 579 582 583
Finite Difference method, centered, convective diffusion equation in two dimensions 257
Finite Difference method, centered, convective diffusion equation, steady state 13—15
Finite Difference method, centered, dispersion diagram 544 549 550 569 574
Finite Difference method, centered, flux-correction 145
Finite Difference method, centered, implicit 77 83 84
Finite Difference method, centered, implicit, unit CFL property 83
Finite Difference method, centered, initial value problem 464 468
Finite Difference method, centered, phase change 66
Finite Difference method, centered, rotating cone problem 349
Finite Difference method, centered, stability 66 78 79
Finite Difference method, centered, truncation error 78
Finite Difference method, centered, unsteady Couette flow 479 483 493
Finite difference method, comparison 41 50 371 386 388 445 469
Finite difference method, dry soil problem 523
Finite difference method, error 502
Finite difference method, exact permeability 519
Finite difference method, Fisher’s equation 389
Finite difference method, melting problem 414
Finite difference method, moving nodes 414
Finite difference method, Navier — Stokes equations 442
Finite difference method, nine-point 528
Finite difference method, reaction 369
Finite difference method, stability 79
| Finite difference method, two dimensions 257—264
Finite difference method, two-point upstream permeability 520
Finite difference method, upstream 28 38 41 44 47 48 51 61 63—65 70 72 73 77 80 88 203
Finite difference method, upstream, 3-point 252
Finite difference method, upstream, adaptive mesh 197 203 205
Finite difference method, upstream, advection equation 31—32 65
Finite difference method, upstream, amplification factor 79
Finite difference method, upstream, Buckley — Leverett problem 508 512 585
Finite difference method, upstream, Burger’s equation 47—48 51—52 70 72 88
Finite difference method, upstream, comparison 49 52 54 67 69 71 88 104 127 128 173 185 332 365 489 503
Finite difference method, upstream, convective diffusion equation 37 38 77 80 582
Finite difference method, upstream, convective diffusion equation, steady state 15 16
Finite difference method, upstream, diagram 543 547 548
Finite difference method, upstream, dispersion 61—62 66
Finite difference method, upstream, dissipation 61—62 66 79
Finite difference method, upstream, dry soil probelm 526 585
Finite difference method, upstream, immiscible displacement 534
Finite difference method, upstream, implicit 77 82
Finite difference method, upstream, linear adsorption 321 327 330 584
Finite difference method, upstream, Navier — Stokes equations 450
Finite difference method, upstream, nonlinear adsorption 336 584
Finite difference method, upstream, permeability 520 531
Finite difference method, upstream, phase change 62 66
Finite difference method, upstream, reaction 360 354 584
Finite difference method, upstream, rotating cone problem 349 350
Finite difference method, upstream, stability 62 66 79
Finite difference method, upstream, unsteady Couette flow 484 585
Finite element method see “Galerkin finite element method”
Finlayson, B. A. 164 165 171 181 186 187 194 212 253—255 259 294 315 317 391 393—396 399 401 463 495 518 521 540
First node 173
Fisher, R. A. 379 399
Fisher’s Equation 379 381
Fisher’s Equation, adaptive mesh 381
Fisher’s Equation, comparison 389
Fisher’s Equation, finite difference method 389
Fisher’s Equation, Galerkin method 389
Fisher’s Equation, MacCormack method 387 388 390
Fisher’s Equation, Taylor — Galerkin method 389
Fisher’s Equation, wave speed 379
Five-spot pattern 527 538
Flaherty, J. E. 218 220 254
Flame problem 385
Flame problem, burner-stabilized 376 381
Flame problem, front, two-dimensional 386
Flame problem, velocity 377 378
Flow, along centerline 470
Flow, compressible 8
Flow, Couette 457
Flow, elongation 458
Flow, laminar 436
Flow, packed bed 43
Flow, partially saturated 517
Flow, past a cylinder 446 447 448
Flow, turbulent 8 434
Flow, two-dimensional cross 343
Flow, two-phase 496
Flow, unsteady Couette 8 474
Flow, water in porous media 517
Fluid, elastic non-Newtonian 458
Fluid, freezing in comer enthalpy method 424 425
Fluid, generalized Newtonian 458
Fluid, incompressible 268 435
Fluid, Newtonian 7 435 458 460
Fluid, non-Newtonian 457 458
Fluid, polymer 7
Fluid, purely viscous 458
Fluid, viscoetaslic 7
Flux correction method 6 137—151 145 183—185 275 277 281
Flux correction method, centered finite difference 141 143
Flux correction method, finite element method 183
Flux correction method, finite element method, Navier — Stokes equations 451
Flux correction method, high-order method 276 280
Flux correction method, low-order method 275 278
Flux correction method, MacCormack 141 143
Flux correction method, Petrov — Galerkin 145
Flux correction method, rationale 152
Flux correction method, solid-body rotation 352
Flux correction method, stability limit 138
Flux correction method, Taylor — Galerkin 146
Flux correction method, two dimensions 275—282
Flux correction method, upstream 140 (see also “Individual methods”)
Flux, “weighted” 421
Fokas, A. S. 516 541
Fokker — Planck equation 3 47 211
Food processing 3 402
Forsyth, G. 23 25 33 46
Fourier analysis 56 94 479 483 494
Fourier transform 57 58 60 180 309 370 480
Fractional flow curve 505 514 531 532
Frauenthal, J. C 534 540
Frechet differential 164
Freeze-coating 3 402
Freezing Pipe 420
Freezing Pipe, moving finite elements 422
Frey, W.H. 287 315
Friedrichs, K. 287 315
Front tracking 288
Fukusako, S. 413 431
Functions, complete set of 19
Functions, orthogonal 19
Furzeland, R. M. 405 432
Galerkin finite element method 3 16—42 93—125 161 184 264 341 351
Galerkin finite element method with interface 430
Galerkin finite element method, advection equation 33 150
Galerkin finite element method, amplification factor 95 96 371
Galerkin finite element method, boundary value method for initial value problem 470
Galerkin finite element method, Buckley — Leverett problem 509 513
Galerkin finite element method, Burger’s equation 53 102 121 122 237 583
Galerkin finite element method, Burger’s equation in two dimensions 272
Galerkin finite element method, comparison 41 53 54 95 97 99 106 110 116 120 127 182 185 234 251 371 386 388 445 468 469 489 503
Galerkin finite element method, comparison with least squares method 233 252
Galerkin finite element method, convective diffusion equation 27 39 40 111 112 117 150 580 582 583
Galerkin finite element method, dispersion 95
Galerkin finite element method, dispersion, diagram 556 561 562 572 576
Galerkin finite element method, dissipation 95 96
Galerkin finite element method, dry soil 526 585
Galerkin finite element method, Fisher’s equation 389
Galerkin finite element method, flux correction 150 538
Galerkin finite element method, flux correction, chemical flooding 539
Galerkin finite element method, fractional-step 449
Galerkin finite element method, geometry, irregular 7
Galerkin finite element method, heat conduction 302
Galerkin finite element method, immiscible displacement 534
Galerkin finite element method, immiscible displacement, comparison 117 121 127 249
Galerkin finite element method, immiscible displacement, unsteady Couette flow 490—495
Galerkin finite element method, implicit 111 116 117
Galerkin finite element method, initial value problem 468
Galerkin finite element method, Lagrangian — Eulerian 451
Galerkin finite element method, linear adsorption 321
Galerkin finite element method, linear trial function 17
Galerkin finite element method, lumped 34
Galerkin finite element method, lumped mass, initial value problem 465 467
Galerkin finite element method, melting problem 414
Galerkin finite element method, mesh, irregular 191
Galerkin finite element method, moving nodes 216 421
Galerkin finite element method, natural boundary conditions 301
Galerkin finite element method, Navier — Stokes equation 438 447
Galerkin finite element method, one-phase problem 404
Galerkin finite element method, phase change problems 421
Galerkin finite element method, polymer centerline problem 471 473
Galerkin finite element method, reaction 371 584
Galerkin finite element method, space-time 412 425
Galerkin finite element method, spectral rotating cone problem 350
Galerkin finite element method, stability 95 110 112 116
Galerkin finite element method, trapezoid rule quadrature 529 532
Galerkin finite element method, truncation error 94
Galerkin finite element method, two dimensional 264—269
Galerkin finite element method, unit CFL property 111
Galerkin finite element method, unsteady Couetle flow 487 493 585
Galerkin finite element method, upstream 105 109
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