Crank J. Free and Moving Boundary Problems
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412
Author index
Mastin, C.
W.
193
Mauersberger, P.
71
Mayers, D. F. 170, 187,
263
Medland,
I.
C. 163,
229
Megerlin, F.
140
Meirmanov,
A.
M. 223,282
Meyer,
G. H. 8,
85,
91, 96, 167, 181, 182,
183, 184, 186, 218, 226, 228, 229,
233
Miellou, J. C.
49
Mikhailov, M.
D.
16,
110
Miller, J. V.
1n,
178, 179,
180
Miller,
K.
180
Mirnate'ghi,
A.
66
Mogel, T. R. 314,
315
Moiseynko, B. D. 228, 229
Morgan, K.
229
Morton, K. W.
1n,178
Mosco,
U.
38
Moskal, M.
S.
223
Motz,
H.
392
Muehlbauer, J.
C. 2
Mullins,W.
W.
15
Murray,
W.
D. 167, 170,
172
Muskat,
M.
16, 31, 297
Neuman,
S.
P. 66, 71,
90,
314, 316, 320,
325,374
Niezgodka,
M.
12,220,222,223,244,281,
282
Nitsche, J. A.
188
Noble, B.
133
Nogi, T. 169
Numerov,
S.
N.
43,287,295
Oberkampf, W.
L.
193, 194
Ockendon, J.
R. 2, 6,
15,21,26,
100, 109,
116-17, 150, 163, 242, 245, 246, 248,
252, 258, 259, 261, 262, 266,
267,
269,
274, 275, 312, 359, 360
Oden, J.
T. 259,
336
O'Leary,
D.
P.
261
Oleinik, O.
A.
217, 220, 222, 223, 224,
243, 246,
281
Ortoleva, P.
150
Osborne, M. R.
94
Outmans,
H.
D.
71,285
Ozis,
T. 312,337,344, 346-7, 352,353
Papanicolau,
G.
259
Patankar,
S.
V.
196
Patel, P. D. 17,
19
Pawlow, I. 281,282
Peckover,
R.
S.
151
Pedroso, R.
I.
156
Pekeris, C. L. 141, 142
Peletier,
L.
A.
110
Phahle, R. D.
201
Phillips, D.
V.
195
Pinkus, O.
93
Pohle,
F.
V.
132
Polubarinova-Kochina, P. Ya. 31, 42, 49,
66, 283, 285, 287, 288, 291, 295, 298,
299, 300, 302, 304, 310, 312, 346, 360,
3n
Poots, G. 132, 136, 137, 139, 150, 156,
202,203
Potter,
D.
207
Pozzi, G. A. 35, 74, 75,
260
Price, R.
H.
217
Primicerio, M. 7,
23-4, 25, 26, 168, 178,
188,244,252,281,282
Pukhnachev, V. V.
282
Quarteroni, A.
81
Radojkovic, M. M.
318
Rahmer, H.
22
Rasmussen,
H.
85, 86, 88, 89, 93, 151,
242,243,385,386,388,389,390
Rathjen, K.
A.
113,
228
Reid, J. D. 315,317
Reid, J. K. 314
Remer, J.
54-5,56,66,70,373,376
Richardson,
S.
81, 82, 109.
243
Riemann,
G.
F. B.-Weber, H.
101
Riley, D.
S.
139, 156,
159
Rippin,
D.
W. T.
315
Risenkampf, B. K. 300
Ritchie,
S.
I. M.
228
Rogers, J. C. W.
54,
100,253,255
Romie,
F. E. 144, 145,
146
Rose, D. J. 314
Rose, M.
E. 141,217,220
Rubinstein,
L.
I. 2, 6, 7, 8, 23-4, 25, 26,
28-9,104,105,117,150,168,222,223,
246, 248, 249,
252
Sacher, P. S. 357,359
Sackett, G. G. 19,
118
Saffman, P. G. 81,
82
Saitoh, T. 167, 197, 198-9,228
Salhani,
D.
93
Samarskii, A. A. 228,
229
Sankar, R. 325, 326, 327,
329
Schafer, E. 226
Schatz,
A.
21,
192
Scheffler, S. 332
Segel,
L.
A.
151
Sekerka, J.
15
Severn, R. T. 203,
228
Shachaf, M.
26,29
Shamsundar,
N.
219,227,228,230,238
Shaug, J. C. 49,
372
Shaw, F.
S.
314,325
Shea,
J. J.
130, 131, 132
Sherman, B. 109, 178, 222
Shishkin,
G.
I.
282
Slack,
M.
R. 217
Slichter, L. B. 141,
142
Sloss, J. M. 22-3, 43, 49, 56, 63, 64, 66,
372
Smith, F.
T.
156
Smith,
G.
D.
314,
315
Sokolov, Ju. D. 298, 300
Solomon, A. D. 2,
6,
7, 140, 141, 142,
143, 144, 163,
281
Southwell, R. V. 314,325,
356
Soward,
A.
M. 161-2
Sparrow, E.
M.
196
Sparrow,
E. W. 219, 228,
230
Sprekels, J.
12
Stampacchia, G.
40,57,60,79,98,100,257
Stefan, J.
1,2,
101, 139,
146
Sternlicht, B.
93
Stewartson,
K.
156, 157, 158, 159-60, 161,
162
Street, R. L. 314, 315
Sunderland,
J. E. 2
Sweet, R. A. 167-8
Symm, G.
T.
317,385
Szekely, J. 117
Tao, L.
N. 10
Tayler,
A. B. 14,
15,21,
110,222
Taylor, C. 314
Taylor, C. J. 91, 321, 322, 323, 324
Taylor,
G.
I.
81,82
Taylor, G. S. 90, 374
Taylor, R. L. 69, 314, 317, 320,
325
Thames, F.
C.
193
Thatcher, R. W. 335-6
Thomas, L. 6
Thompson, C. P.
181
Thompson, J. F. 193
Tichonov,
A.
N.
23
Tien, L. C.
171
Tien, R.
H.
239
Todsen, M. 90
Torelli, A. 63, 90, 91, 93,
99
Trefftz,
E.
317
Trent,
J. S.
281
Turland,
B.
D.
15(}-1,
199,206,207,209-
Author
iIIda
413
10,211
Turski, L.
A.
15
Valli,
A.
57
Varga, R. 314, 315
VarogIu, E. 336, 337, 338, 339, 341.
342,
343
Vasilev,
F.
P.
169
Vedernikov, V. V. 298,300
Verma,
R.
D.
90
Visintin, A.
8(}-1,
93, 244
Voller,
V.
R.
233,235,236,237,239,247
Volpi, G. 35
Waddington, J. F. 226,228
Waechter, R.
T.
156, 157, 158, 159-60,
161
Wait, R. 314, 332
Weber, H. 287
Wellford,
L.
C.
173
Wendroff, B. 204
Westwater,
J. 6
Westwater, J. W.
171
Whiteman,
J.
R. 332
Wiener, J. H. 106, 107
Williams, J.
183
Williams, R.
E.
320
Williams, W.
E. 220
Wilson,
D.
G.
2, 10, 105, 106, 107,108,
127,141,
163,249,281,282
Wilson, G.
199
Winslow,
A.
M.
193,
197
Witherspoon, P. A. 66, 71, 90, 314, 316,
320, 325,
374
Wollkind, D. J.
151
Wood, A. S.
228
Wrobel, L. C. 318
Wu, T.
S.
126
Wu, Y.
S.
318
Yagoda, H. P. 126
Yanenko, N.
N.
314
Young, D. M. 314
Youngs,
E.
G. 70
Yuen,
W.
W. 130, 170
Zaslavsky,
D.
289
Zienkiewicz, O. C. 195,317
Zygmund,
A.
161
Subject index
abl~tion
defined
11
laser-cutting 151-5
space vehicle alloys
12
ablation problems
enthalpy formulation of
252
integral-equation formulations for
126,
127
method of lines with SOR algorithm
186
absorption functions, oxygen diffusion 23
accretion
75
allowance for
286
adaptive meshes
173
adaptive variational formulation, numerical
solution 337-43
air-liquid interfaces, enthalpy functions
for
251
algorithms
Alt 92, 376-84
APT
254
Cottle 357-9
Cryer
46,75.77,359-72
D02AJF
191
Fox-Sankar 325-9
Gear
191
outer iteration built into 46,
52,
368
SOR
see
successive overrelaxation
also
see
numerical algorithms
alloy solidification problems
6,
14-16
enthalpy method 245-9
Green's functions used in 117,118
similarity solutions for
110
stability analysis of 150-1
alloys
ablation of
12
diffusionlheat
flow
in 14-16
Alt algorithm
92,
376-84
alternating direction method 183-4
alternating method, split-domain prob-
lem
56
alternating-phase truncation (APT)
method 253-7
analytical solutions 101-62
seepage problems 283-312
annular electrochemical machining prob-
lems 85-6, 385-93
anode profile, electrochemical machining
89,385-93
appearing/disappearing phases, Stefan
problem
178
approximate methods, analytical, solu-
tion 283-8
approximate solutions
139-62
fictitious diffusivity approximation 147-
50
inverse Stefan problem, 144-7
perturbation method 150-62
spatial subdivision 142-4
steady-state approximation
139-42
approximate trial solutions, computation
of 314-19
aquifers 60-3,362
arbitrary-shaped dams 52-4, 376-9
with toe drain 54-7
asymptotic formulations
concentrated capacity
26
perturbation method
150
axisymmetric
flow
problems 28-9, 31, 66-
70,318,372-6
disc-in-cylinder 326-9
wells
318, 372-6
Baiocchi transformation
arbitrary-shaped dam
53
with toe drain 55-6
axisymmetric well
flow
67-8,
373
capillary-fringed rectangular dams
77
coastal aquifer
61
electrochemical machining
86
evaporation 74-5
general statement
of
96-100
pond seepage 70, 373-4
rectangular dam
with sheetpile
44
with toe drain 41-2
simple rectangular dams 34-8
sloping-base dam
51
stratified dam 72,
73
stream functions incorporated into 40-1
three-dimensional dams
57,58
Baiocchi
transformation-continued
transient
dam
90, 92, 93
Baiocchi variables
form
of
98-100
three-dimensional boundary conditions
for 59
biological problems, numerical solution
of
8
biquadratic finite elements 175-6
blob model, mushy region 6
Boadway transformation
204-6, 344, 348
body heating
239-42
body-fitted curvilinear coordinates 89,
192-5
example
of
use
of
195-9
boundary conditions
dam
seepage 32-3
moving interfaces
3-4
representation
of
381
boundary
element
methods
317
boundary position
comparison
of
various methods
for
deter-
mination
of
233-4
melting problem 136-7
oxygen diffusion 20
solution
of
217
boundary singularities 332-6
boundary-fixing
coordinate
transformation,
boundary-position determined by
233-4
boundary-fixing methods 187-216
boundary-tracking methods 163-86
boundary-value problems, defined
1
Boussinesq equations 285-7
Brezis formulation, generalized
dam
problem
79-80,92
canals, seepage from
63-{j
capillary fringe
76-9
degree
of
saturation for 377
capillary rise 76
capillary tissue, oxygen diffusion in
22
cathodes, electrochemical machining 85,
88,390
Cauchy-Riemann
equation
34,41
cavitation
disc-in-cylinder 325-9
journal bearing
93-{j
chemical activity 246
circular electrodes, numerical solution
for 388-9
circular porous
dam,
seepage through 347-
53
classical Stefan
problem
see
Stefan problem
coastal aquifers 60-3
Cryer algorithm for
36-2
collapse, solid-phase 12-13
Subject index
415
comparison
theorem,
embedding 127
compatibility conditions 368-72
arbitrary-shaped
dam,
with
toe
drain 56
dam
with iulet face slanted 48, 371-2
open
channel
64,65
rectangular dam
with capillary fringe 78
with sheetpile
45,368-71
sloping-base
dam
50
complementarity formulation, two-
dimensional
dam
49
complementarity methods, numerical
solutions 355-76
computer programs, boundary-fixing itera-
tive algorithm
191
computers, parallel 359
concentrated thermal capacities
23-9
concentration discontinuity 245
concentric circular electrodes, numerical
solution for 388-93
conformal transformations 293-7, 298,
299,300
conjugate gradient
method
261
connections, free-boundary problem 100
conservation
of
energy, Stefan
problem
10
conservative difference schemes 207,
210-
11
constant surface cooling,. series solutions
for 126
constant-rate solidification, temperature
expression 2, 144-7
convection, Stefan
problem
10
convection terms,
method
of
lines
181
convective boundary conditions
variable time step finite-difference
method applied
to
170
convergence
theorem
proofs
Cryer algorithm 356
enthalpy
method
226
convolution integrals 132
convolution
theorem,
inversion by 155
coordinate transformation 93, 189
cosine integral transforms 127
Cottle fast algorithm 357-9
Crank-Nicolson scheme
boundary-fixing in 189-90,
191
complementarity methods used
with 268-9
generalization
of
173
truncation methods used with 268-9
Cryer algorithm
coastal aquifer 362
definition
of
356
evaporation 75
finite-difference
and
finite-element forms
of
359-72
416
Subject index
Cryer algorithm-(!ontinued
lubrication cavitation
94
rectangular dam
with capillary fringe
77
with sheetpile
46
simple dam problem 360-2
stratified dams
363
also see successive overrelaxation
crystal growth 142,
251
crystal packing, mushy region 6-7
crystallization, supercooled melt
104
cubic splines method 143, 172
curvi1inear coordinates 89, 192-9
temperatures interchanged with
2m
cylinder, freezing inside and outside
of
170
cylinder problem
constant-rate solidification 144-5
enthalpy method for 237-8
cylindrical coordinates, similarity solutions
in
111
cylindrical pipes, solidification
of
liquid
around
137
dams
arbitrary-shaped 52-4, 376-9
with toe drain 54-7
evolution
33,90-7
generalized expression 79-81
impervious base 75,365
porous base
75
rectangular see rectangular dams
simple
see
simple dam
slanted exit face
54
slanted inlet face 47-9, 54,
371
with toe drain 49, 371,
372
sloping base 50-2
stratified 71-4, 336, 363, 383-4
three-dimensional 57-60, 353-5, 366-7
transient 90-1
Darcy's law 32, 81,
283
decision theory, examples 1
degenerate free-boundary problems 81-93,
282
degeneration, phase 12-14
degree of saturation
capillary fringe
377
representation
of
381
dendrite formation 6,
15
density changes, Stefan problem
10
detachment point, defined
32
determinantal equations, trial free-boundary
method
327
dimensionless heat parameters, Stefan
problem 9, 156-7
dimensiouless latent heat 9,
157
values
of
102,
149
dimensionless solidification time
237
Dirac delta functions
118,
218,
227
Dirichlet boundary data 37-8,
320,
365,
375
Dirichlet conditions 45, 47, 321,
391
Dirichlet-type problem
386
disc-in-cylinder
flow
problems 326-9
discharge
axisymmetric well
69
coastal aquifer 62,
63
dam seepage
34
discontinuous enthalpy functions 228-9,
280
distributed array processor (DAP)
359
ditches, seepage from 63-6, 297-300,
343
divergence theorem proof, enthalpy
method 219
D02AJF
algorithm
191
double-iterative scheme
capillary-fringed dam
78
dam with sheetpile
368
dam with slanting inlet face
371
dam with toe drain 371,
372
sloping-base dams
372
drains, seepage into 63-5
drawdown, transient seepage problems
following 92,
324
drying
of
porous region, similarity solutions
for
110
Duhamel integrals
132
Duhamel's theorem
123
Dupuit approximation 283-5,287
Duvaut transformation
270, 271,
276
electrochemical machining (ECM) 85-9,
109,
384-93
electrochemical machining problems
formulation
of
85-9
integral-equation methods for 384-93
numerical solutions for 385-93
electron beams, hole-cutting
by
151-5
elliptic electrodes, numerical solution
for 389-90
elliptic equations
1,30,81,
150
elliptic variational inequalities
defined 258
electrochemical machining
87
Hele-Shaw injection
84
elliptic variational inequality, solution
of
265
embedding technique, 122-8
enthalpy functions
alternative forms
of
226-8
discontinuous 228-9
form
of
217-19
enthalpy methods 217-53
alloy solidification
15,
245-9
enthalpy methods-continued
conditions not amenable
to
252-3
electrochemical machining
85
explicit finite-difference schemes 223-6
moving-boundary position 233-5
other methods compared with 233-5
weak solutions of 217,220--3
equilibrium diagrams, alloy solidifica-
tion 14-15,245
equipotential boundary, hodograph
plane
289
equipotential lines, variable-inter-
change 342-3
equipotential transformations
197
error-function solutions 2, 102-3, 112-13,
128
Euler's constant
159
eutectic diagrams 14-15,245
evaporation
ablation problems 151-5
porous
flow
problems 74-5
evolution dam problems 33,
9~3,
99
exact solutions, defined
101
examples, free and moving boundary
problems 1
explicit finite-difference methods
boundary-fixing transformation
188
enthalpy 223-6
fixed grid
168
isotherm migration 212-13,216
explicit moving-boundary conditions
190
fictitious boundary conditions 122-3
fictitious diffusivity approximations 147-50
fictitious heat parameters
148
fictitious temperatures, fixed finite-
difference grid
167
fictitious-point approximations, boundary-
fixing
197
filtration problem, similarity solutions
for
110
finite-difference methods
dam problems
43
embedding techniques comparedwith
128
finite-element methods compared
with 315-16,
366
fixed grid 163-8
laser hole-cutting
155
modified grid 168-81
rectangular dam, with capillary fringe
78
unequal space interval 164
variable space-grid
17~3
variable time step 168-70
finite-element methods
adaptive mesh 173-81
dam problems
43
finite-difference methods compared
Subject index
417
with 315-16,
366
transient dam
90,91,92
finite elements, triangulation
380
five-sixths rule 180
fixed finite-difference grids 163-8
fixed-domain methods 35-8,217-82
flame-front prob,ems 249-51
diffusionlheat
flow
in
16
flow
analogy, Hele-Shaw 16, 81-2, 109,
243
fluid injection 82
fluid transfer, semi-permeable mem-
brane 8
Forchheimer equations
286
Fourier-series solutions
oxygen diffusion problem 187,
263
single-phase Stefan problem
117
Fox-Sankar algorithm 325-9
Frechet derivative
188
free-boundary moving methods 319-29
free-boundary problems
defined
1,30
formulated 31-100
numerical solution of 313-93
freezing, axial line source
111
freezing fronts, coupling 274-5
freezing index
259,270,272,280
Fremond freezing index 259,270,272,280
Frenet formulae 330
front-fixing methods 187-216
front-tracking methods 163-86
fully penetrating wells 67-9,
318
Dupuit formulae applied to
285
Galerkin formulations 173, 178, 180, 318,
322
Garabedian modified boundary condi-
tions 329-32
gas bubbles
dissolution
of
170
electrochemical machining
89
gas dynamics, examples 1
Gauss-Seidel iteration 184, 230,
356
Gear
algorithm
191
general solutions, Stefan problem 2
generalized enthalpy functions 242,
243
glass manufacture
108
global basis functions
318
global methods, free-boundary mov-
ing 325-9
Goodman integral method 128-33, 134
variable time step finite-difference
method compared with
170
graded grids, trial free-boundary
method
315
graphical solutions
concentrated capacity 27-8
418
Subject index
graphical solutions-continued
two-dimensional problem
279
variable-interchange method
343
Green's functions 113, 117-21
laser hole-cutting
154
Green's theorem
dam with inlet face slanted
48
integral-equation method starting
from 385,
391
multi-dimensional problem 138,
139
simple rectangular dam 36,
37
Stefan phase-change boundary
conditions
175
grid spacing, trial free-boundary
method 315-17
ground-water
flow
81, 283, 300
ground-water pollution
63
Hamel transformation 295-7
heat balance, ice-water interface 5
heat
flow
problems
Green's functions used in 117-21
integral methods used
in
128
heat
flux
jumps
173,
217
heat-balance integral method 128-33,
134
with spatial subdivision 133-7
heat-flow equation
IMM form
of
212
non-dimensional form
of
211
Heaviside function, generalized dam
problem
80
Hele-Shaw
flow
analogy 16, 81-2, 109
enthalpy formulation
of
243
Neumann's solution for 109
Hele-Shaw injection 82-5
heterogeneous porous media 70-4
hodograph method 288-93
conformal transformations 293-7, 298,
299,300
simple dam problems 291,297
trapezoidal drainage ditch 297-300
homogenization, Stefan problem 8
hopscotch scheme
enthalpy formulation
228
truncation method combined with
257
horizontally stratified dams 71-2, 73-4,
383-4
hot liquid injection, oil-saturated
media
23,28
hydraulic conductivity 32
hyperbolic equations, weak solution of
217
hyperbolic represemation of
heat conduction 117
moving boundary
113
ice see melting ice
ice cubes, heat
flow
in water of
12
ice formation, steady-state approximation
of
141-2
images, method
of
see
method of images
imbedding methods, invariant 133-4, 184-
6,233
immiscible fluids, moving boundary problem
in
16
impermeable medium
oscillating temperatures in 27-8
porous strata in
23-4
impervious boundary, hodograph
plane
289
impervious-base dams 75,
365
Boussinesq equations for
286
implicit boundary conditions, Stefan
problem 19-23,
118
implicit methods
discontinuous enthalpy functions 228-9
isotherm-tracking along orthogonal
flow
lines 215-16
solidification boundary 167-8
implicit moving-boundary conditions 190-
1
impurities, alloy
14
infiltration
75
inhomogeneities
axisymmetric
flow
67
stratified media
71
injection, Hele-Shaw 82-5
injection moulding 82
instabilities, moving boundary
150
instability region, alloy
15
insulated cathode sections, electrochemical
machining 88-9
integral methods, free-boundary mov-
ing 324-5
integral transforms 114-17
integral-equation formulations, numerical
solution
of
317,385-93
integral-equation methods 114-39,384-93
electrochemical machining 85, 89, 385-
93
embedding technique 122-8
Goodman integral method 128-33,
134
Green's functions 113, 117-21
heat-balance method 128-33,
134
with spatial subdivision 133-7
integral transforms 114-17
multi-dimensional problem 137-9
interfaces
examples of 109-10
melting 2-4
invariant imbedding methods 133-4, 184-6
two-phase Stefan problem
233
inverse formulation, coordinate inter-
change 353-5
inverse Stefan problem 11-12, 144-7
inverse transformations
hodograph method 294-5
single-phase Stefan problem 115
iron, recrystallization
of
114, 143
iron-carbon alloys, solidification
of
118
irregularly shaped domains, finite elements
for 316
isoparametric curvilinear coordinates
195
isoparametric finite elements 174
isotherm migration method (IMM) 199--216,
344
linear complementarity method compared
with 274-5
multi-dimensional 201-16
complete transformation
of
vari-
ables 204-11
orthogonal flow lines 211-16
partial transformation
of
vari-
ables 201-4
one-wmensional
199--201
Jacobi-type iterative process 345,350-1
joule heating 239-40
journal bearings, lubrication cavitation
in
93-6,98
jump conditions, flame-front 249-50
jump discontinuities
enthalpy method
217,219,226
multi-phase crystallization
106
sloping-base dam with sloping inlet
face
51
Kantorovitch expansion
93
Kirchhoff transformation 219,
281
Kozeny transformation
43
Kuhn-Tucker conditions 260, 267
Lagrange multiplier method
261,274
Lagrangian interpolation formulae 164,
166
lake freezing problem, integral equations
for
117
Langer model
of
alloy solidification
15
Laplace equation
axisymmetric wells 67
boundary-fixing 193, 194
circular porous dam 352
electrochemical machining 86, 392
impervious-base dams 365
integral-equation expression
of
384
simple rectangular dam 32
trapezoidal dam seepage region 337
trial free-boundary method 330
Laplace transforms
approximate solutions 153, 154, 158, 159
laser hole-cutting 153, 154
single-phase Stefan problem 114,
115
Subject index
419
Laplacian operator, replacement in Baiocchi
transformation
97
laser beams, hole formation by 11, 151-5
latent-heat approximations 2, 140, 229
Laurent series
304
linear complementarity methods
isotherm migration methods compared
with 274-5
truncation methods compared with 267-
9
linear complementarity problems
equations for 357
Hele-Shar injection
85
lubrication cavitation 94
numerical solution
of
355-76
linearized forms, generalized Stefan
problem
8
lines, method
of
see
method
of
lines
lubrication, journal bearing 93-6
lumped-parameter interpretation, fixed grid
temperatures
167
mapping, hodograph 291-5
Megerlin method 140, 142,
143
melt depths 127
melt-pool growth, reactor substrate
209
melting interfaces 2-4
position
of
136-7
melting-ice problem 2-4, 99
allowable temperature range for
143
embedding techniques used for 122
heat-balance integral method 129
Neumann's solution
101
method
of
images 132, 161-2
method
of
lines
boundary-position determined by 233-4
electrochemical machining
85
journal bearing lubrication 96
with Ricatti transformation 186
with
SOR
algorithm 184-6
Stefan problem time-dependency re-
moved by
343
transient dams
91
minimization formulations
axisymmetric well 69
capillary-fringed rectangular dam 77
coastal aquifer 62
electrochemical machining 87
simple dam problem 39-40, 361-2
stratified dam 73, 74
variational inequality 265-6, 356, 364
modified boundary conditions,
Garabedian 329-32
modified grids 168-81
modified heat parameters 248
modified velocity potentials 32, 41,
57
420
Subject index
moving, free-boundary 319-29
global methods of 325-9
integral methods of 324-5
local methods of 319-24
moving finite-element method 180-1
moving grid systems 171-3
moving heat sources, similarity solutions
and 111-14
moving-boundary problems
defined 1
formulated 2-29
multi-dimensional problems
enthalpy
funCtions
in 228-35
enthalpy method for 218-19
heat-balance integral method applied
to 137-9
multiple penetration depths
132
multiple-well problems 70,
318
Murray-Landis variable grid 170-1
mushy regions 5-6,239-41
alloy solidification
249
spot welding 5,237,239-41
Muskat problem
16
NAG algorithms
191
negative latent heats
109
Neumann conditions
45,47,271,321,391
Neumann's solution 101-10
Newton linearization 233,234
Newton-Raphson iteration 341,
343
Newton-type iterative process 136,
320
Newton's three-eighths rule
120
nodal enthalpy determination 236-7
node positioning, finite-element 179-80
non-dimensional variables, Stefan prob-
lem
9,156-7
non-linear heat parameters 5-S
non-linear instabilities, alloy solidifica-
tion
15
non-linear Stefan problems
148
non-orthogonal transformations 193-5
normals to isotherms, geometrical proce-
dure to determine 213-14
numerical algorithms
arbitrary-shaped dams
54
coastal aquifer
62
dam with inlet face slanted
48
generalized dam problem
79,
376
rectangular dam
with sheetpile 45,
46
with toe drain and sheetpile
46
simple dam 34-5,38
transient dam
91
numerical methods
general description of
163
rectangular dam with capillary fringe
78
simple rectangular dams
35
numerical solutions 313-93
concentrated capacity
26
rectangular dam with sheetpile 45-6
well
problem
69
Oberkampf transformations
194,
196,
197
oil production methods 23, 28,
29
one-dimensional problems
boundary-fixing transformations
for
187-92
density changes in
10
finite-element methods applied to
173,
175-S
integral-equation formulations
ill
117
journal bearing lubrication
96
melting
129,
187
method of lines 184-6
solidification
111
variable time step finite-difference
methods for
169
weak solution for 220-1
one-dimensional Stefan problem
discontinuous \finite-element method
for 175-S
truncation method 253-4
weak solution for 222
one-dimensional two-phase Stefan problem
finite-element method
173
method of lines 181-6
smoothed enthalpy functions in
227
one-parameter integral method 137-9,
202-3
one-phase
see
single-phase
open channels, seepage from 63-6
orthogonal
flow
lines, isotherm movement
along 211-16
orthogonal transformations
192
oscillating temperatures, concentrated
capacity 27-8
oxygen dittusion problem
boundary-fixing transformations for
187-8
capillary tissue 22, 98-9
Cottle fast algorithm used in
359
embedding technique used in
127
enthalpy method for 244
finite-element method
178
Green's functions used in
118
implicit boundary conditions in 19-23,
118
Lagrangian formulae in
166
moving grid systems 171-3
truncation method 255-7
two-dimensional
21
oxygen diffusion problem--continued
variable time step finite-difference
method for
170
variational approach 260, 263-4
parabolic equations 1,
81
parabolic inequalities 258-9,
266
paraffin sediments, melting of 23,
28
parallel computer, complementarity prob-
lems solved using
359
partially penetrating wells
69
partially unsaturated
flow,
algorithm
for 376-84
Patel condition
17,91,168
IMM
form of
202
three-dimensional extension of
206
penetration depths 132-3,
142
penultimate nodes, modified grid
179
permeabilities
stratified porous media
71
well-soil
67
perturbation methods 150-62, 287,
288
phase boundaries
conditions on 10, 25,
105,
106
heat jumps at 173,217,221
isotherm expression of
199,
214
location of
164,
175
position determined
by
enthalpy
method 235-9
shape of 126-7,
139
Stefan problem 2
phase change problem, weak solution
of
225
phase changes, concentrated thermal
capacities
23--9
phase degeneration 12-14
phase diagrams 14-15
piecewise-constant functions 224-5
point of detachment, defined
32
Polubarinova-Kochina solution 300-12
change of variables in
310
equipotential dam face with impervious
base
305
free surface intersecting inlet face 306-7
free surface joining linear seepage
face
306
free-boundary coordinates
311
parameters in
311
seepage face joining outlet face
305
polygonal approximation, integral-equation
method 386-7
pond, seepage from 66, 70,
373
porous base dams, infiltration through
75
porous media
concentrated thermal capacity of
23-4
examples of
flow
through
30
stratification of
71
Subject index
421
power series solution, single-phase Stefan
problem
116
pre-heating times, laser hole-cutting
153
pre-melting problem, heat-balance method
applied to
130
precipitation problem, enthalpy method
in
228
pressure functions, generalized dam
problem
80
prism, finite-element 364-5
prism solidification
integral-equation method, 137-9
isotherm migration method 201-2,
214
quadrilateral finite efements
173
quasi-steady-state models
dam seepage
287
electrochemical machining
85,
87-8,
89,
242,385
solidification
139
quasi-variational inequality, arbitrary-
shaped dam 52,
54
radial coordinates, boundary
fixing
in
197-
8
radiation conditions
123-4
Rayleigh-Ritz expansion
93
reactor substrate, melt-pool growth in
209
recrystallization of iron 114,
143
rectangular dams
capillary-fringed 76-7
with sheetpile 44-6,321,
382
and toe drain
46
simple
see
simple dam
with toe drain 41-4,
324
recurrence relation, heat-balance
method
135
regional numerical methods
318
regula-falsi
methods
188,
326,
328
reservoir heights, rapid change of
92,
324
Reynolds' equation, journal bearing
lubrication
95
Ricatti transformations
182,
186
Riemann P-equation
302,
307
Riemann zeta-function
160
Runge-Kutta method
131,
137,
143
saturated
flow
30,31
saturation, degree of
377,
381
Schatz transformation
21
Schwarz-Christoffel transformations 293-
4,299
secant method
368
arbitrary-shaped dam
56
open channel seepage
65