The Mathematics of Fluid Flow Through Porous Media - Myron B. Allen, III

Скачать книгу

102

      106  103

      107  104

      108  105

      109  106

      110  107

      111  108

      112  109

      113 110

      114  111

      115  112

      116  113

      117  114

      118  115

      119  116

      120  117

      121  118

      122  119

      123  121

      124  122

      125  123

      126 124

      127  125

      128  126

      129  127

      130  128

      131  129

      132  130

      133  131

      134  132

      135  133

      136  134

      137  135

      138  136

      139  137

      140  138

      141  139

      142 140

      143  141

      144  142

      145  143

      146  144

      147  145

      148  146

      149  147

      150  148

      151  149

      152  150

      153 151

      154  152

      155  153

      156  154

      157  155

      158  156

      159  157

      160  158

      161  159

      162  160

      163  161

      164  162

      165  163

      166  164

      167  165

      168  166

      169  167

      170  168

      171  169

      172  170

      173  171

      174  172

      175  173

      176  174

      177  175

      178  176

      179  177

      180  178

      181  179

      182  180

      183  181

      184  182

      185  183

      186 184

      187  185

      188  186

      189  187

      190  189

      191 190

      192  191

      193  193

      194  194

      195  195

      196 196

      197  197

      198 198

      199 199

      200 200

      201 201

      202 202

      203 203

      204 204

      205 205

      206 206

      207  207

      208 208

      209 209

      210 210

      211 211

      212 212

      213  213

      Seldom turns out the way it does in the song.

      Robert Hunter

      This book provides a semester‐length course in the mathematics of fluid flows in porous media. Over a 20‐year span, I taught such a course every few years to doctoral students in engineering, mathematics, and geophysics. Most of these students' research involved flow and transport in groundwater aquifers, soils, and petroleum reservoirs. The students' mathematical backgrounds ranged from standard undergraduate engineering requirements to more advanced, graduate‐level training.

      The book emphasizes analytic aspects of flows in porous media. This focus may seem odd: Most mathematically oriented scholarship in the area is computational in nature, owing both to the heterogeneity of natural porous media and to the inherent nonlinearity of many underground flow models. Nevertheless, while many superb books cover computational methods for flows in porous media, intelligent design of numerical approximations also requires a grasp of certain analytic questions:

       Where do the governing equations come from?

       What physics do they model, and what physics do they neglect?

       What qualitative properties do their solutions exhibit?

      Where appropriate, the book discusses numerical implications of these questions.

Скачать книгу