Applied mathematics in hydrogeology:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Lewis
1999
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 382 S. |
| ISBN: | 1566703751 |
Internformat
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Datensatz im Suchindex
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| adam_text | APPLIED MATHEMATICS IN HYDROGEOLOGY TIEN-CHANG LEE DEPARTMENT OF EARTH
SCIENCES UNIVERSITY OF CALIFORNIA RIVERSIDE, CALIFORNIA LEWIS PUBLISHERS
BOCA RATON LONDON NEW YORK WASHINGTON, D.C. CONTENTS PREFACE 1
CONSERVATION EQUATIONS 1 1.1 HEAT CONDUCTION 1 1.1.1 HEAT ENERGY 1 1.1.2
FOURIER S LAW 3 1.2 GROUNDWATER FLOW 5 1.2.1 EQUATION OF CONTINUITY 5
1.2.2 DARCY S LAW . . 6 1.2.3 FLOW EQUATION 8 1.3 ADVECTIVE HEAT
TRANSFER 11 1.4 DISPERSION EQUATION ; 12 1.5 BOUNDARY AND INITIAL
CONDITIONS 13 1.6 PROBLEMS, KEYS, AND SUGGESTED READINGS 15 1.7
NOTATIONS 19 2 SOURCE FUNCTIONS AND CONVOLUTION 21 2.1 HEAT SINK AND
SOURCE 21 2.1.1 INSTANTANEOUS POINT SOURCE 21 2.1.2 INSTANTANEOUS LINE
SOURCE 22 2.1.3 STEADY LINE SOURCE 23 2.2 CONVOLUTION 24 2.2.1 CONCEPT
25 2.2.2 EXPERIMENTAL IMPULSE RESPONSE 26 2.2.3 NUMERICAL CONVOLUTION 27
2.2.4 TRANSFER FUNCTION 28 2.2.5 FAST FOURIER TRANSFORM 29 2.2.6
Z-TRANSFORM 30 2.3 THEIS WELL FUNCTION 31 2.3.1 ASSUMPTIONS 31 2.3.2
DERIVATION 33 2.3.3 DETERMINATION OF TRANSMISSIVITY AND STORATIVITY . .
. . 35 2.3.4 SEMILOG METHOD 36 2.3.5 RADIUS OF PUMPING INFLUENCE 37
2.3.6 RECOVERY TEST 37 2.4 LINEAR SUPERPOSITION OF WELL FUNCTIONS 38
2.4.1 PUMPING NEAR A CONSTANT HEAD BOUNDARY 38 2.4.2 PUMPING NEAR AN
IMPERMEABLE BOUNDARY 40 2.4.3 PUMPING NEAR TWO DISSIMILAR MEDIA 40 2.5
EVALUATION OF EXPONENTIAL FUNCTION 40 2.6 PROBLEMS, KEYS, AND SUGGESTED
READINGS 43 2.7 NOTATIONS 54 3 LAPLACE AND HANKEL TRANSFORMS 55 3.1
FUNDAMENTALS OF THE LAPLACE TRANSFORM 55 3.1.1 TRANSFORM PAIRS 55 3.1.2
BASIC TRANSFORM FORMULAS 56 3.2 CONTOUR INTEGRATION 60 3.2.1 SINGULARITY
60 3.2.2 RESIDUE THEOREM : 63 3.2.3 MULTIVALUED FUNCTION 64 3.2.4
EXAMPLE 1: BRANCH CUT, NO SINGULARITY 65 3.2.5 EXAMPLE 2: BRANCH CUT,
SINGULARITY 69 3.2.6 EXAMPLE 3: CONVOLUTION 1 72 3.2.7 EXAMPLE 4:
CONVOLUTION 2 73 3.2.8 EXAMPLE 5: RATIONALIZATION 75 3.2.9 EXAMPLE 6: A
SERIES REPRESENTATION 75 3.2.10 EXAMPLE 7: ROOTS, NO BRANCH CUT 76
3.2.11 EXAMPLE 8: BRANCH CUT, LOGARITHM 77 3.2.12 EXAMPLE 9: BESSEL
FUNCTIONS - DELTA FUNCTION 78 3.3 NUMERICAL INVERSION 79 3.3.1
GAVER-STEHFEST METHOD 80 3.4 HANKEL TRANSFORM 81 3.4.1 BESSEL FUNCTIONS
81 3.4.2 EXAMPLE 1H: HANKEL TRANSFORM - USING A SERIES . . . . 85 3.4.3
EXAMPLE 2H: HANKEL TRANSFORM OF L/(A 2 + Q 2 ) 86 3.4.4 EXAMPLE 3H:
HANKEL TRANSFORM OF J 0 [AR }/ (A 2 + Q 2 ) . . 87 3.4.5 EXAMPLE 4H:
HANKEL TRANSFORM OF AJ^AR J/IA 2 + Q 2 ) . . 88 3.4.6 EXAMPLE 5H:
INVERSE HANKEL TRANSFORM 1 89 3.4.7 EXAMPLE 6H: INVERSE HANKEL TRANSFORM
2 92 3.4.8 EXAMPLE 7H: INTEGRATION INVOLVING L/- /L * Z 2 93 3.4.9
NUMERICAL HANKEL TRANSFORM 97 3.5 PROBLEMS, KEYS, AND SUGGESTED READINGS
100 3.6 NOTATIONS 112 DRAWDOWN IN CONFINED AQUIFERS 113 4.1 THEIS WELL
FUNCTION 114 4.2 STEADY-STATE SOLUTION 116 4.2.1 JACOB SOLUTION 116
4.2.2 THIEM S FORMULA 116 4.3 FULL-PENETRATION PUMPING WELL, R W ^ 0 117
4.3.1 FORMULATION 117 4.3.2 LAPLACE-DOMAIN SOLUTION 118 4.3.3
TIME-DOMAIN SOLUTION 119 4.4 HANTUSH S LEAKY AQUIFER 121 4.4.1
ASSUMPTIONS ; 122 4.4.2 MASS BALANCE EQUATION 122 4.4.3 FULL-PENETRATION
PUMPING WELL, R W = 0 124 4.4.4 FULL-PENETRATION PUMPING WELL, R W ^ 0
127 4.4.5 PARTIAL-PENETRATION PUMPING WELL, R W = 0 129 4.4.6
PARTIAL-PENETRATION PUMPING WELL, R W =FI 0 132 4.5 LEAKAGE AS BOUNDARY
FLUX 134 4.5.1 FULL-PENETRATION PUMPING WELL, R W = 0 135 4.5.2
PARTIAL-PENETRATION PUMPING WELL, R W = 0 141 4.5.3 PARTIAL-PENETRATION
PUMPING WELL, R W ^ 0 144 4.6 SLUG TEST 145 4.6.1 FULL-PENETRATION WELL
146 4.7 PROBLEMS, KEYS, AND SUGGESTED READINGS 148 4.8 NOTATIONS 157
DRAWDOWN IN UNCONFINED AQUIFERS 159 5.1 DUPUIT-FORCHHEIMER THEORY 160
5.1.1 LATERAL FLOW 160 5.1.2 STEADY RADIAL FLOW 161 5.2 PUMPING WELLS OF
INFINITESIMAL DIAMETER 161 5.2.1 FULL-PENETRATION PUMPING WELL, R W = 0
162 5.2.2 PARTIAL-PENETRATION PUMPING WELL, R W = 0 169 5.3 PUMPING WELL
OF NONZERO DIAMETER 171 5.3.1 FULL-PENETRATION PUMPING WELL, R W ^ 0 172
5.3.2 PARTIAL-PENETRATION PUMPING WELL, R W ^ 0 . . . . . . . 178 5.3.3
EFFECT OF FINITE DIAMETER 179 5.4 WELL STORAGE AND SKIN EFFECT 180 5.4.1
FULL-PENETRATION WELL 180 5.4.2 PARTIAL-PENETRATION WELL 184 5.5
PROBLEMS, KEYS, AND SUGGESTED READINGS 189 5.6 NOTATIONS 194 HEAT
TRANSFER AND GROUNDWATER FLOW 197 6.1 ADVECTIVE HEAT TRANSFER 198 6.1.1
STEADY VERTICAL FLOW 200 6.1.2 STEADY HORIZONTAL FLOW 203 6.1.3 LATERAL
GRADIENT DT/DX = CONSTANT 205 6.2 HEAT SOURCES IN REGIONAL GROUNDWATER
FLOW 207 6.2.1 INSTANTANEOUS POINT SOURCE 207 6.2.2 CONTINUOUS POINT
SOURCE .209 6.2.3 INFLUENCE OF GROUND SURFACE : ; 210 6.3
TOPOGRAPHY-CONTROLLED FLOW 212 6.3.1 CONSERVATION EQUATIONS 212 6.3.2
STEADY GROUNDWATER FLOW ... 214 6.3.3 TEMPERATURE DISTRIBUTION 216 6.4
HEATING AND PRESSURIZATION 220 6.4.1 EQUATION FOR FLUID PRESSURIZATION
221 6.4.2 PRESSURIZATION 223 6.5 PROBLEMS, KEYS, AND SUGGESTED READINGS
226 6.6 NOTATIONS 235 SOLUTE TRANSPORT 237 7.1 FORMULATION OF EQUATIONS
237 7.1.1 ADSORPTION 239 7.2 ONE-DIMENSIONAL PROBLEMS 241 7.2.1 EXAMPLE
1: A STEP INPUT 241 7.2.2 EXAMPLE 2: EXPONENTIALLY DECAYING INPUT 243
7.2.3 EXAMPLE 3: A SYSTEM WITH RETARDATION 245 7.2.4 EXAMPLE 4: A
REACTIVE SYSTEM 246 7.2.5 EXAMPLE 5: A REACTIVE AND RETARDATIVE SYSTEM .
. . . 248 7.2.6 .EXAMPLE 6: ADVECTION AT BOUNDARY, A^A 248 7.2.7 EXAMPLE
7: ADVECTION AT BOUNDARY, X = A 253 7.2.8 EXAMPLE 8: A PULSE INPUT 254
7.2.9 EXAMPLE 9: ADVECTION, TRANSFER FUNCTION 255 7.3 TWO-DIMENSIONAL
PROBLEMS 257 7.3.1 EXAMPLE 10: A PLANE DISPERSION MODEL 257 7.3.2
EXAMPLE 11: ONE IMPERMEABLE BOUNDARY 262 7.3.3 EXAMPLE 12: BOUNDED FLOW
263 7.4 THREE-DIMENSIONAL PROBLEMS 264 7.4.1 GREEN S FUNCTION 265 7.4.2
INTEGRAL TRANSFORMS 265 7.5 RADIAL DISPERSION 267 7.5.1 FORMULATION 267
7.5.2 SOLUTION 268 7.6 SIMULATION BY Z-TRANSFORM 271 7.6.1 EXAMPLE 13:
NUMERICAL SIMULATION 271 7.7 PROBLEMS, KEYS, AND SUGGESTED READINGS 272
7.8 NOTATIONS 278 8 SOLVING AX = B 279 8.1 ELEMENTARY MATRIX OPERATIONS
279 8.2 EIGENPROBLEMS 281 8.2.1 EIGENMATRIX 281 8.2.2 LEAST-SQUARES
METHOD 283 8.3 X = A- X B 284 8.3.1 GAUSSIAN ELIMINATION AND
BACKSUBSTITUTION 284 8.3.2 LU DECOMPOSITION 286 8.3.3 ITERATION METHODS
287 8.4 SINGULAR VALUE DECOMPOSITION 289 8.5 EXAMPLES 294 8.5.1 EXAMPLE
1: SVD 294 8.5.2 EXAMPLE 2: 111-CONDITIONED MATRIX 296 8.5.3 EXAMPLE 3:
ILL-CONDITIONED MATRIX (CONTINUED) . . . . 298 8.5.4 EXAMPLE 4: A
WELL-BEHAVED MATRIX 298 8.6 PROBLEMS, KEYS, AND SUGGESTED READINGS 299 9
FINITE ELEMENT ANALYSIS 305 9.1 ID FINITE ELEMENT METHOD 305 9.1.1
FORMULATION OF A PROBLEM .. . 305 9.1.2 GALERKIN WEIGHTED RESIDUAL 307
9.1.3 ELEMENTARY MATRICES . . . .* 310 9.1.4 FINITE-ELEMENT EQUATION 311
9.1.5 DIFFERENTIAL EQUATION IN TIME 314 9.1.6 LUMPED FINITE-ELEMENT
FORMULATION 316 9.1.7 NATURE OF COEFFICIENT MATRIX 317 9.1.8 INITIAL AND
BOUNDARY CONDITIONS 317 9.1.9 SOURCE TERM 318 9.1.10 NUMERICAL
INSTABILITY AND OSCILLATION 319 9.2 2D FINITE ELEMENT METHOD 322 9.2.1
PROCEDURES 322 9.2.2 REMARKS 326 9.3 TRANSPORT EQUATIONS 328 9.3.1
ADVECTIVE HEAT TRANSFER 328 9.3.2 SOLUTE TRANSPORT 330 9.4 PROBLEMS,
KEYS, AND SUGGESTED READINGS 333 10 INVERSE PROBLEMS 337 10.1 LINEAR
INVERSION 338 10.1.1 EXAMPLE 1: A LINEARIZABLE SYSTEM 339 10.1.2
EXAMPLE 2: PARTIALLY LINEARIZABLE 342 10.2 CONSTRAINED LINEAR INVERSION
343 10.2.1 CONSTRAINT OF PARAMETERS 343 10.2.2 MORE ON BIASED LINEAR
INVERSIONS 348 10.2.3 GOODNESS OF FIT 349 10.3 NONLINEAR INVERSION 353
10.3.1 GAUSS-NEWTON METHOD 354 10.3.2 RESOLUTION 356 10.3.3 RIDGE
REGRESSION . 356 10.4 EXAMPLE: A ID FINITE-ELEMENT PROBLEM 357 10.5
SUGGESTED READINGS 360 APPENDIX: NOTES ON EQUATION SOLVING 361 A.I
INTEGRAL TRANSFORMS 361 A.2 SEPARATION OF VARIABLES 363 A.3 SERIES
SOLUTIONS 363 A.4 LINEAR SUPERPOSITION 364 A.5 NUMERICAL METHODS 364 A.6
INTEGRATION 365 BIBLIOGRAPHY 367 INDEX 375
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| spelling | Lee, Tien-Chang Verfasser aut Applied mathematics in hydrogeology Tien-Chang Lee Boca Raton [u.a.] Lewis 1999 382 S. txt rdacontent n rdamedia nc rdacarrier Hydrogeologie - Angewandte Mathematik - Lehrbuch Mathematik Hydrogeology Mathematics Angewandte Mathematik (DE-588)4142443-8 gnd rswk-swf Hydrogeologie (DE-588)4026307-1 gnd rswk-swf Hydrogeologie (DE-588)4026307-1 s Angewandte Mathematik (DE-588)4142443-8 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008645405&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lee, Tien-Chang Applied mathematics in hydrogeology Hydrogeologie - Angewandte Mathematik - Lehrbuch Mathematik Hydrogeology Mathematics Angewandte Mathematik (DE-588)4142443-8 gnd Hydrogeologie (DE-588)4026307-1 gnd |
| subject_GND | (DE-588)4142443-8 (DE-588)4026307-1 |
| title | Applied mathematics in hydrogeology |
| title_auth | Applied mathematics in hydrogeology |
| title_exact_search | Applied mathematics in hydrogeology |
| title_full | Applied mathematics in hydrogeology Tien-Chang Lee |
| title_fullStr | Applied mathematics in hydrogeology Tien-Chang Lee |
| title_full_unstemmed | Applied mathematics in hydrogeology Tien-Chang Lee |
| title_short | Applied mathematics in hydrogeology |
| title_sort | applied mathematics in hydrogeology |
| topic | Hydrogeologie - Angewandte Mathematik - Lehrbuch Mathematik Hydrogeology Mathematics Angewandte Mathematik (DE-588)4142443-8 gnd Hydrogeologie (DE-588)4026307-1 gnd |
| topic_facet | Hydrogeologie - Angewandte Mathematik - Lehrbuch Mathematik Hydrogeology Mathematics Angewandte Mathematik Hydrogeologie |
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