The variants were designed to add small increments of

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ystems. These advantages and additional calculations relative to the standard WEL Package, however, come with a price—specifically the potential for increased computational effort and time, as well as increased memory requirements. To provide a perspective on these computational costs, a range of test cases were run and timed to illustrate relative computational times. The test cases were all variations of the Reilly problem described previously in this report and all tests included only one multi-node well having 12 nodes. The variants were designed to add small increments of complexity with each successive test case to provide a measure of the computational cost associated with selected features and processes documented in this report. All of these tests assume the properties listed in tables 2 and 3. For consistency, however, all scenarios tested here use the value of KSKIN = 12.5 ft/d as listed in table 3. All tests were solved numerically using the Preconditioned Conjugate Gradient (PCG) method with a head change closure criterion of 1×10-5, a residual change closure criterion of 0.10, a maximum number of inner iterations of 30, and a maximum number of outer iterations of 20. All transient flow cases were run with an initial steady-state stress period followed by one 365-day transient flow stress period in which the desired discharge from the multi-node well was set at Q = -4,400 ft3/d. The transient stress periods were always discretized into 20 time steps using a time-step multiplier of 1.1. All tests were run with both the MODFLOW–2000 and MODFLOW–2005 versions of the code on the same personal computer—a Dell workstation with a 3.6 gigahertz Intel Pentium 4 processor and 3 gigabytes of random access memory (RAM). The Fortran code was compiled under Intel Fortran Compiler Integration for Microsoft Visual Studio 2005, version 10.0.3718.2005. The results of the computational efficiency tests are listed in table 4. The first test is for the relatively simple case of steady-state flow, which requires just one time step and one stress period; the calculated heads are illustrated in figure 6. In this case, there was no net discharge from the multi-node borehole, although intraborehole flow was allowed to occur. The solution converged after 393 iterations and required about 24 seconds of central processing unit (CPU) time (for an average computational time of 0.061 seconds per iteration) for both MODFLOW–2000 and MODFLOW–2005. One of the general findings of these tests is that MODFLOW–2005 is consistently slower than MODFLOW–2000 by an average of about 7 percent. In the first test the intraborehole flow caused some small flux between the well and the aquifer at each of the 12 nodes of the well. When these identical fluxes are simulated using 12 single-node wells in the standard MODFLOW WEL Package rather than with one multi-node well, the numerical solution actually required about 12 percent more iterations and computational time. (The WEL Package input was easily generated using the WEL1 flag in the MNWI Package.) The remaining cases tested assumed that a 365-day transient-flow stress period followed the steady-state stress period. In the first of these, the total cumulative number of Acknowledgments 41 Table 4. Computational effort for range of variations of Reilly test problem. [Abbreviations used: central processing unit, CPU; cubic feet per day, ft3/d; feet, ft] Time per iteration, in seconds Test Description of variation of Reilly problem MODFLOW– MODFLOW– MODFLOW– MODFLOW– MODFLOW– MODFLOW– 2000 2005 2000 2005 2000 2005 1 Steady-state flow with MNW2 393 393 24 24 0.061 0.061 2 Steady-state flow with WEL Package 440 440 25 26 0.057 0.059 3 Transient with MNW2, Q = -4,400 ft3/d 3,563 3,574 182 202 0.051 0.057 4 Transient with well package 3,505 3,455 187 212 0.053 0.061 5 Transient, MNW2, three nearby wells (Q = -4,000 ft3/d each) 5,584 5,542 287 308 0.051 0.056 6 Same, with partial penetration fraction = 0.2 in node 1 5,442 5,437 270 303 0.050 0.056 7 Same as 5, with constraints and hlim = -7.5 ft, Qfrcmn = 0.10, Qfrcmx = 0.20 6,527 6,513 331 349 0.051 0.054 8 Same as 5, with two lowest nodes offset vertically (nonvertical well) 5,364 5,378 276 293 0.051 0.054 9 Same as 5, but pump capacity option active 5,983 5,986 315 340 0.053 0.057 10 Same as 5, with minimal output 5,584 5,542 284 307 0.051 0.055 Cumulative iterations iterations and the total computational time increased by nearly a factor of 10 (test 3 in table 4). When this test was rerun representing the 12 nodes of the multi-node well by 12 singlenode wells (test 4), the simulation ran slightly more efficiently (though it should be noted that the distribution of discharge values among the 12 nodes could not be predetermined using the standard WEL Package and that with MNW2 the flows at the nodes may change each time step whereas flows are fixed during a stress period with the standard WEL Package). When three single-node pumping wells...
View Full Document

This document was uploaded on 01/20/2014.

Ask a homework question - tutors are online