Groundwater flow modelling (450008) - Python web page
Groundwater flow modelling (450008)
Computer laboratories
dr. V.E.A. Post
Contents
Part I: Python
1
1 Calculating heads
5
1.1 Solution methods . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.1.1 Gauss-Seidel iteration using a spreadsheet . . . . . . . . . 5
1.1.2 Gauss-Seidel iteration using Python . . . . . . . . . . . . 6
1.1.3 Successive over relaxation . . . . . . . . . . . . . . . . . 8
1.1.4 Direct solution . . . . . . . . . . . . . . . . . . . . . . . 8
1.2 Regional flow example . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.1 No-flow boundaries . . . . . . . . . . . . . . . . . . . . . 10
2 Calculating flows
13
2.1 Water budgets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Abstraction well . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3 Transient simulations
17
3.1 Abstraction well (transient) . . . . . . . . . . . . . . . . . . . . . 17
Part II: MODFLOW
19
4 Well field in a river valley
21
Part III: MicroFEM
27
5 Well in a semi-confined aquifer
29
6 Infiltration canal
33
Part IV: Linear algebra
37
7 Systems of linear equations
39
7.1 Linear equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
7.2 Systems of linear equations . . . . . . . . . . . . . . . . . . . . . 40
3
8 Matrices
45
8.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
8.2 Special matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
8.3 Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
8.4 Determinant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
8.5 Cramer's rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
8.6 Inverse of a matrix . . . . . . . . . . . . . . . . . . . . . . . . . 51
References
53
Part I: Creating finite difference models in Python
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