Introduction to Numerical Methods for Water Resources (Oxford Science Publications Series) Book

	Notation
1	Surface and groundwater flow - types of equation	1
1.2	Surface flow - friction laws	3
1.3	Surface flow - lateral velocity distribution	5
1.4	Shallow-water equations	7
1.5	The kinematic wave equation	11
1.6	Pollution transport in rivers	16
1.7	Groundwater flow	19
1.8	Effect of an abstraction well	24
2	The method of characteristics	28
2.2	Application of the method	30
2.3	The numerical method of characteristics	31
2.4	The method of characteristics used for the numerical solution of the St Venant equations	36
3	Finite difference methods	40
3.2	Ordinary differential equations - initial value problems	40
3.3	Stability	44
3.4	Convergence	50
3.5	Ordinary differential equations - boundary value problems	52
3.6	Partial differential equations - elliptic boundary value problems	56
3.7	Initial value problems - parabolic equations	60
3.8	The advection-diffusion equation	64
3.9	Initial value problems - hyperbolic equations	68
3.10	Stability and convergence illustrated on the box scheme	71
3.11	The finite volume or cell-differencing method	74
4	Numerical solution of surface flow equations by finite differences	75
4.2	The non-linear kinematic wave equation	76
4.3	The numerical solution of the St Venant equations	79
4.4	Limitations on the use of the box scheme	88
4.5	Methods for two-dimensional surface flow	89
5	Finite difference methods applied to groundwater flow	94
5.2	Steady-state groundwater flow-elliptic boundary value problems	94
5.3	Boundary conditions	98
5.4	Time-dependent groundwater flow - parabolic problems	99
5.5	Noise problems with ephemeral streams	104
6	The finite element method	112
6.2	The finite element matrices	117
6.3	Some other types of element	125
6.4	Isoparametric elements	129
6.5	Accuracy, convergence, superconvergence	131
6.6	Numerical integration in the finite element method	133
6.7	The patch test	139
7	Groundwater flow problems solved by finite elements	148
7.2	Aquifer models - general considerations	149
7.3	Aquifer models - general procedure	152
7.4	Aquifer models - initial conditions	156
7.5	Mass balance	157
7.6	Modelling a phreatic surface	162
7.7	The numerical solution of Richards' equation	165
7.8	Choice of hillslope finite element grid	170
7.9	Initial conditions for a hillslope model	176
7.10	Three-dimensional groundwater flow	183
8	Boundary integral methods	185
8.2	The boundary integral method	185
8.3	Groundwater flow round a tunnel with permeable invert	192
8.4	Electromagnetic river gauging	196
9	Water-quality modelling	202
9.2	Surface flow - water-quality modelling	204
9.3	Subsurface flow - gradient recovery methods	209
9.4	Water-quality modelling in subsurface flow	210
9.5	Salt water intrusion problems	211
10	Dimensionless parameters	220
10.2	The Buckingham pi theorem	223
	Appendix 1. Vertical integration of groundwater flow equations	230
	Appendix 2. Methods for solving simultaneous equations	234
	Appendix 3. Noise problems	237
	References	239
	Author index	249
	Subject index	252