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Mode FlowTable of Contents
Description:UNIPASS™ provides a complete generic interface example with full installation option. By default, all the required files for this example are installed in the following directory: C:\Program Files\Unipass\Examples\External\ModeFlow The sample files would run as is unless the users have installed the example files in a different directory than the one specified above. MODFLOW-2000, a public domain software maintained by the U.S. Geological Survey [ 3] is installed in C:\Program Files\Unipass\Examples\External\ModeFlow\bin All the source codes and documentation for MODFLOW-2000 is packed in the following self-extracting file: C:\Program Files\Unipass\Examples\External\ModeFlow\Modflow\mf2k1_0.exe MODFLOW is a computer program that numerically solves the three dimensional ground-water flow equation for a porous medium by using a finite –difference method. A new version of MODFLOW, called MODFLOW-2000, which is designed to accommodate the solution of equation in addition to the ground-water flow equation. Figure 1 1 MODFLOW-2000 illustration depicting common components modeled
Figure 2 Finite difference discretization of MODFLOW example Consider the under ground water flow problem illustrated in Figure 2. Constant pressure is specified along the boundary of the reservoir, possible a river or a lake. Water inflow in the form of rain and denoted as ‘recharge’ permeates the top layer. Water outflow is divided between the draining ditch, various pumps (not shown), the reservoir, and the two layers of sand aquifers below. Further details of the under ground water flow model can be found in Reference [ 4]. Listings of all the input files can be found in Reference [ 3 ] starting with page 89. The random variables used to model the uncertainties of the parameters are listed in Table 1. The purpose of this analysis is to predict the probability of water that accumulates in the system exceeding a prescribed allowable amount (i.e. a flood situation). Table 1 Uncertainties modeled in the MODFLOW-2000 example
Back to TopDefining A Distribution For Each ParameterOpen the following sample file with UNIPASS™: “C:\Program Files\Unipass\Examples\External\ModeFlow\modflow_example2.PAS” Open the Variable Definition Window and review the distributions defined for this model. For instruction on how to modify these distributions please refer to Reference [ 1]. The variable window with all the distributions for this problem are shown in Figure 3. Figure 3 Distribution defined for MODFLOW-2000 example Back to TopDefining The Parametric FilesOpen the parametric file editor and load the file ‘twri.bc6’ into the editor as shown in Figure 4. Figure 4 Loading the sample input file ‘twri.bc6’ into the parametric file editor Note that all the random variables defined are listed in the top left window. Select ‘TRPPY1’ from the list and highlight the second numeric field in the third line of the parametric file editor (see Figure 5). Figure 5 Selecting a variable and an associated field in the parametric file editor Next, double click ‘TRPY1’ in the random variable list, the highlighted field in the parametric file editor show be replaced with ‘TRPY1’ enclosed by brackets (see Figure 6). This creates a template for UNIPASS™ to insert a value into this field every time it prepares the input file ‘twri.bc6’. Repeat the same procedure for HY1, VCONT1, and VCONT2. A sample parametric file was saved as ‘backflow.par’. Do not overwrite this file without verifying the contents. Figure 6 Creating a template for a single distribution in the parametric file editor Backflow.par
Recharge.par
Back to TopDefining External ResponseOpen the external response window. All the parameters have already been defined. Hover the mouse right above the command line and hold, a small window will pop up to show the entire content of this item (see Figure 7). The batch file ‘twri.bat’ is just a batch file to start MODFLOW-2000. Click once on the command line icon and the complete command line including the input and the output file name will appear in the tiny status window on the bottom left (see Figure 7). The parametric file, the input file, and the output file have already been defined as ‘backflow.par’, ‘twri.bc6’ and ‘twri.lst’ respectively. Right click on any item in the tree to see a menu of all the available operations.
Figure 7 Generic interface definition for MODFLOW-2000 Only one values will be extracted from the output file ‘twri.lst’. Because the output file format actually changes with the number of iteration MODFLOW used, a fix format interface would fail. Instead, three keyword search instructions have been specified. Double click on the first keyword: ‘VOLUMETRIC BUDGET FOR ENTIRE MODEL’. A window will ask to load the file ‘twri.lst’. Click yes and the file will be loaded. Immediately after, the first keyword string will be located and selected in the display to the right.
Figure 8 Locating the first keyword defined for external(1) Double click on all the search commands and verify the correct response value are highlighted. External.in
Defining Limit State FunctionOpen the function definition window
Figure9 Limit state function definition Only one limit state function has been defined using the external function. The allowable value for this model is 300. Only one cutest is required for this component problem. For more details on function definition refer to [ 1 ]. Keep all the default parameters and run the solver. The result is shown in Figure 10.
Figure 10 Animation of PDF of the limit state function for the MODFLOW-2000 example (at the end of 100 iterations) Back to TopFailure ProbabilityBy 100 sampling points in the Monte Carlo Simulation,
PDF/CDF of Limit-State Function
Back to TopExample of SensitivityNormalized Factor:
Plot of (s)d(Pf)/d(m)
Plot of (s)d(Pf)/d(s)
Back to TopReferences:[ 1 ] ” UNIPASS™Quick Start Guide Version 4.2”, 2002, PredictionProbe, Newport Beach, CA. [ 2 ] Mary C. Hill, Edward R. Banta, Arlen W. Harbaugh, and Evan R. Anderman, “MODFLOW-2000, The U.S. Geological Survey Modular Ground-Water Model —User Guide To The Observation, Sensitivity, And Parameter-Estimation Processes And Three Post-Processing Programs”, U.S. Geological Survey, Open-File Report 00-184. [ 3 ] Arlen W. Harbaugh, Edward R. Banta, Mary C. Hill, Michael G. McDonald, MODFLOW-2000, “The U.S. Geological Survey Modular Ground-Water Model—User Guide to Modularization Concepts And The Ground-Water Flow Process”, U.S. Geological Survey, Open-File Report 00-92. [ 4 ] Harbaugh, A.W., and McDonald, M.G., 1996a, “User's documentation for MODFLOW-96, an update to the U.S. Geological Survey modular finite-difference ground-water flow model: U.S. Geological Survey Open-File Report 96-485”, 56 p.
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Last Updated 02/08/10
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