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A Finite-Element Program for the Simulation of Three- Dimensional Aquifers

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A Finite-Element Program for the Simulation of Three- Dimensional Aquifers FEMFLOW3D: A Finite-Element Program for the Simulation of Three- Dimensional Aquifers. Version 1.0 By T. J. Durbin and LD. Bond U.S. GEOLOGICAL SURVEY Open-File Report 97-810 CO CO o CO Sacramento, California 1998 U.S. DEPARTMENT OF THE INTERIOR BRUCE BABBITT, Secretary U.S. GEOLOGICAL SURVEY Thomas J. Casadevall, Acting Director The use of firm, trade, and brand names in this report is for identification purposes only and does not constitute endorsement by the U.S. Geological Survey For additional information write to: Copies of this report can be purchased from: "District Chief U.S. Geological Survey U.S. Geological Survey Information Services Placer Hall Box 25286 6000 J Street Federal Center Sacramento, CA 95819-6129 Denver, CO 80225 CONTENTS Abstract ................................................................. 1 1.0 Introduction ........................................................... 2 2.0 General Features of FEMFLOW3D ........................................... 3 3.0 Description of FEMFLOW3D ............................................... 5 3.1 Program FEMFLOW3D ............................................. 7 3.1.1 Background ............................................... 7 3.1.2 Mathematical Basis ......................................... 7 3.1.3 Structure of Subroutine ....................................... 7 3.2 Subroutine MODEL ................................................ 7 3.2.1 Background ............................................... 7 3.2.2 Mathematical Basis ......................................... 7 3.2.2.1 Governing Equation ................................. 7 3.2.2.2 Finite-Element Approximation ........................... 9 3.2.2.3 Interpolating Function ................................ 14 3.2.2.4 Integration in Time .................................. 19 3.2.2.5 Iterative Solution ................................... 20 3.2.3 Structure of Subroutine ...................................... 20 3.2.3.1 General Structure ................................... 20 3.2.3.2 Compressed Storage ................................. 22 3.2.3.3 Linear Problems .................................... 24 3.2.3.4 Finite-Element Grid ................................. 24 3.3 Subroutine CHEAD ............................................... 27 3.3.1 Background .............................................. 27 3.3.2 Mathematical Basis ........................................ 27 3.3.3 Structure of Subroutine ...................................... 30 3.4 Subroutine FLUX ................................................. 30 3.4.1 Background .............................................. 30 3.4.2 Mathematical Basis ........................................ 31 3.4.3 Structure of Subroutine ...................................... 32 3.5 Subroutine RIVER ................................................ 33 3.5.1 Background .............................................. 33 3.5.2 Mathematical Basis ........................................ 33 3.5.3 Structure of Subroutine ...................................... 36 3.6 Subroutine EVAP ................................................. 38 3.6.1 Background .............................................. 38 3.6.2 Mathematical Basis ........................................ 38 3.6.3 Structure of Subroutine ...................................... 41 3.7 Subroutine VFLUX ................................................ 42 3.7.1 Background .............................................. 42 3.7.2 Mathematical Basis ........................................ 42 3.7.3 Structure of Subroutine ...................................... 46 3.8 Subroutine FAULT ................................................ 48 3.8.1 Background .............................................. 48 3.8.2 Mathematical Basis ........................................ 48 3.8.3 Structure of Subroutine ...................................... 51 3.9 Subroutine SINK ................................................. 52 3.9.1 Background .............................................. 52 3.9.2 Mathematical Basis ........................................ 52 3.9.3 Structure of Subroutine ...................................... 55 3.10 Subroutine WATER ............................................... 57 3.10.1 Background ............................................. 57 3.10.2 Mathematical Basis ........................................ 62 3.10.3 Structure of Subroutine ..................................... 62 Contents III 3.11 Subroutine LAND ................................................ 66 3.11.1 Background ............................................. 66 3.11.2 Mathematical Basis ........................................ 66 3.11.2.1 Effective Precipitation ............................... 66 3.11.2.2 Infiltrated Water ................................... 67 3.11.2.3 Distribution of Infiltrated Water ........................ 67 3.11.2.4 Nonuniform Applications ............................. 73 3.11.3 Structure of Subroutine ..................................... 74 3.12 Subroutine BUDGET .............................................. 74 3.12.1 Background ............................................. 74 3.12.2 Mathematical Basis ........................................ 74 3.12.3 Structure of Subroutine ..................................... 75 3.13 Subroutine SHAPE ............................................... 75 3.13.1 Background ............................................. 75 3.13.2 Mathematical Basis ........................................ 75 3.13.3 Structure of Subroutine ..................................... 75 3.14 Subroutine BAND ................................................ 76 3.14.1 Background ............................................. 76 3.14.2 Mathematical Basis ........................................ 76 3.14.3 Structure of Subroutine ..................................... 78 3.15 Subroutine SOLVE ............................................. 79 3.15.1 Background ............................................. 79 3.15.2 Mathematical Basis ........................................ 79 3.15.3 Structure of Subroutine ..................................... 82 3.16 Subroutine SEARCH .............................................. 82 3.16.1 Background ............................................. 82 3.16.2 Mathematical Basis ........................................ 84 3.16.2.1 Modified Box-Kanemasu Method ....................... 84 3.16.2.2 Interface with Subroutine MODEL ...................... 89 3.16.3 Structure of Subroutine ..................................... 90 3.17 Subroutine SOLEQU .............................................. 90 3.17.1 Background ............................................. 90 3.17.2 Mathematical Basis ........................................ 91 3.17.3 Structure of Subroutine ..................................... 92 3.18 Subroutine FMERGE .............................................. 93 3.18.1 Background ............................................. 93 3.18.2 Mathematical Basis ........................................ 93 3.18.3 Structure of Subroutine ..................................... 93 4.0 Model validation ....................................................... 94 4.1 Transient, Confined, Radial Flow to a Well .............................. 94 4.1.1 Problem Description ........................................ 94 4.1.2 Model Simulation .......................................... 95 4.1.3 Results ................................................. 97 4.2 Transient, Unconfined, Radial Flow to a Well ............................. 98 4.2.1 Problem Description ........................................ 98 4.2.2 Model Simulation ......................................... 100 4.2.3 Results ................................................ 102 4.3 Transient, Confined, Linear Flow to a Ditch ............................. 104 4.3.1 Problem Description ....................................... 104 4.3.2 Model Simulation ......................................... 104 4.3.3 Results ................................................ 106 4.4 Transient Compaction Owing to Water-Level Changes ...................... 107 4.4.1 Problem Description ....................................... 107 4.4.2 Model Simulation ......................................... 107 4.4.3 Results ................................................ 110 IV Contents 5.0 Input Formats ........................................................ Ill 5.1 File-Specification File ............................................ Ill 5.1.1 Files for Subroutine MODEL ................................. 117 5.1.2 Files for Subroutine WATER ................................. 118 5.1.3 Files for Subroutine SEARCH ................................ 120 5.2 Subroutine MODEL Input File ....................................... 121 5.2.1 Simulation Parameters (MODEL) .............................. 121 5.2.2 Time-Step Scheme (MODEL) ................................ 122 5.2.3 Output Controls (MODEL) .................................. 125 5.2.4 Matrix Solution Parameters (SOLVE) ........................... 126 5.2.5 Finite-Element Grid Coordinates (MODEL) ....................... 126 5.2.6 Finite-Element Grid Incidences (MODEL) ........................ 128 5.2.7 Aquifer Parameters (MODEL) ................................ 129 5.2.8 Initial Hydraulic Heads (MODEL) ............................. 131 5.2.9 Specified-Head Boundary Condition (CHEAD) .................... 133 5.2.10 Internal and Boundary Fluxes (FLUX) .......................... 135 5.2.11 River-Aquifer Interactions (RIVER) ...........................
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