1. implicit     t = 0.07
                                        FROM MODFLOW
   t      h2      h3      h4      h2      h3      h4      q at right ft³/day x 10^-2

0.07   8.13   7.90   7.02     8.13   7.90   7.02   6.83
0.14   8.00   7.54   6.32     8.00   7.54   6.32   5.44
0.21   7.86   7.22   5.88     7.86   7.22   5.88   4.56
0.28   7.72   6.95   5.59     7.72   6.95   5.59   3.97
0.35   7.60   6.73   5.38     7.60   6.73   5.38   3.56
0.42   7.50   6.55   5.23     7.49   6.55   5.23   3.27
0.49   7.40   6.41   5.12     7.40   6.41   5.12   3.05
0.56   7.33   6.30   5.04     7.33   6.30   5.04   2.88
0.63   7.27   6.21   4.98     7.27   6.22   4.98   2.75
0.70   7.22   6.15   4.93     7.22   6.15   4.93   2.65


and the same list again 1. implicit     t = 0.07
to compare with               FROM EXPLICIT

   t       h2      h3      h4      h2      h3      h4

0.07     8.13   7.90   7.02     8.20   8.20   6.05
0.14     8.00   7.54   6.32     8.20   7.20   5.91
0.21     7.86   7.22   5.88     7.73   7.07   5.43
0.28     7.72   6.95   5.59     7.64   6.62   5.34
0.35     7.60   6.73   5.38     7.42   6.50   5.12
0.42     7.50   6.55   5.23     7.35   6.29   5.05
0.49     7.40   6.41   5.12     7.25   6.21   4.95
0.56     7.33   6.30   5.04     7.21   6.11   4.91
0.63     7.27   6.21   4.98     7.16   6.06   4.86
0.70     7.22   6.15   4.93     7.13   6.01   4.83


2. implicit     t = 0.14

  t        h2        h3        h4

0.14     7.95   7.45   6.46   8.00   7.54   6.32
0.28     7.67   6.84   5.65   7.72   6.95   5.59
0.42     7.43   6.41   5.23   7.50   6.55   5.23
0.56     7.26   6.14   5.00   7.33   6.30   5.04
0.70     7.14   5.96   4.86   7.22   6.15   4.93


3. Compare Mass Balance for 0.07 and 0.14 day time steps:

implicit     t = 0.07                                                   t=0.14
   t      VOL_left     Stor      VOL_right   Mass Bal   VOL_left     Stor        VOL_right  Mass Bal
0.07   9.8E-05   4.7E-03   4.8E-03     -8.4E-03                                        
0.14   2.8E-04   3.6E-03   3.8E-03     +1.1E-02   6.9E-04   8.2E-03   8.0E-03     +1.0E-01
0.21   4.8E-04   2.7E-03   3.2E-03     -5.0E-03                                        
0.28   6.7E-04   2.1E-03   2.8E-03     -5.0E-03   1.5E-03   5.1E-03   5.7E-03     +1.3E-01
0.35   8.4E-04   1.7E-03   2.5E-03     -8.0E-04                                        
0.42   9.8E-04   1.3E-03   2.3E-03     -5.3E-03    2.2E-03   2.0E-03   4.6E-03     -1.0E-01
0.49   1.1E-03   1.1E-03   2.1E-03     +2.0E-02                                        
0.56   1.2E-04   7.8E-04   2.0E-03     -9.0E-03    2.6E-03   1.5E-03   3.9E-03     +6.3E-02
0.63   1.3E-04   6.3E-04   1.9E-03     -5.6E-16                                        
0.70   1.4E-04   4.8E-04   1.9E-03     -5.4E-03    3.0E-03   1.3E-03   3.5E-03     +1.9E-01

smaller time steps provide a better mass balance when transients are strong because the varying conditions are better approximated by taking smaller steps

4. graphing for time step = 0.07 days



close up, notice it is smoother than the explicit result below:

explicit result for comparison:


here is the MODFLOW result:


close up:

and the implicit result again for comparison with MODFLOW's result above


and further in time to help you assess when steady state is reached:


5. Comparison

Head decreases steadily with time and the rate of decrease is reduced at later times for both time step sizes. The implicit solution is more stable and, we expect, more accurate given the good mass balances and similar results for different time step sizes. Also the similarity of the implicit results and those of MODFLOW, which has been tested comprehensively, gives us confidence in our calculations.