Slice-Successive Overrelaxation Package (SOR1)

Slice-Successive Overrelaxation Package (SOR)

Last modified on Wednesday, January 31, 1996 - 6:58:34 PM

Skip forward to Input instructions for the Slice-Successive Overrelaxation Package.

The original instructions for the Slice-Successive Overrelaxation Package are on page 13-10 of McDonald and Harbaugh (1988).

Introduction: The Slice-Successive Overrelaxation Package is one of several options for solving the finite difference approximation of the fundamental equations governing groundwater flow in MODFLOW. Other options include the Strongly Implicit Procedure and the Preconditioned Conjugate Gradient Package. The solutions obtained with any of these solvers should be similar although the time required to find the solution and the amount of memory used may differ. The Slice-Successive Overrelaxation Package is not a good choice if you wish to use the rewetting capability of BCF2 or BCF3. The Preconditioned Conjugate Gradient Package is usually best although the Strongly Implicit Procedure may also work.

There is one parameter, ACCL, that can be varied in the Slice-Successive Overrelaxation to change how rapidly it converges to a solution. Unfortunately, we don't know ahead of time what value of this parameters will lead to the most rapid solution.

ACCL usually is set between 1 and 2. If the model diverges from the solution or shows frequent oscillation, ACCL may be too high. If the model converges monotonically toward the solution, ACCL may be too low. In the latter case, the program may terminate execution prematurely. The program stops when the maximum change in head between successive iterations is lower than some user-defined value. If ACCL is too low, the differences in head between successive iterations will also be low even if the computed heads are far from ideal.

Once you have obtained a value of ACCL for the Slice-Successive Overrelaxation Package that work well, it will probably also work well with most variations of the model.

Use of Slice-Successive Overrelaxation with two dimensional profile models may have some advantages. The procedure uses a direct approach to solve the finite difference equations for each of a series of vertical slices through the model and then iterates through the slices to reach a final result. In two dimensional profile models, there need be only one slice and it can be solved in a single iteration. Thus with a properly oriented profile model, an exact solution of the finite difference equations can be found in a single iteration. To take advantage of this characteristic, the profile model must be along a single row rather than along a single column. It is possible that roundoff error will have a greater effect if a direct approach is used.

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Input Instructions All input parameters should be right justified

Line 1
- Spaces 1-10, MXITER, Integer, Maximum number of iterations per time step. 50 is usually enough.
Line 2
- Spaces 1-10, ACCL, Real Number, The "acceleration parameter" is usually set between 1 and 2.
- Spaces 11-20, HCLOSE, Real Number, Head change criterion for convergence
- Spaces 21-30, IPRSOR, Integer, printout interval

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Line 1, Spaces 1-10, MXITER, Integer

On each time step MODFLOW will go through a series of iterations as it approaches an acceptable solution. Sometimes, however, the program may enter an infinite loop. To prevent this, MXITER forces the program to terminate after a number of iterations. If this happens, MODFLOW has not reached a solution and the results should not be accepted as a good estimate of the groundwater flow. Instead the input needs to be modified to avoid this problem. Often the problem is with the conceptual model. You should go back and check that your conceptual model is reasonable. Drying and rewetting of cells with the BCF2 or BCF3 packages is also a frequent culprit. Usually 50 iterations is enough to reach an acceptable solution.

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Line 2, Spaces 1-10, ACCL, Real Number

The "acceleration parameter" is usually set between 1 and 2. It governs how fast the model approaches the solution. If too high, the model may overshoot and either diverge or show frequent oscillations. If too low, the program will approach the solution monotonically and may not reach a sufficiently accurate solution before the program stops.

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Line 2, Spaces 11-20, HCLOSE, Real Number

When the maximum change in head between two iterations is less than HCLOSE, the program will assume that it has obtained a sufficiently accurate solution and stop. Sometimes, this criterion can be incorrect (see ACCL). It is always a good idea to examine the water budget for each time step. A large error (>1%) in the water budget could indicate that the program terminated prior to reaching a solution. It could also be a problem with the General-Head Boundary Package

or the Stream Package. Go back to Input instructions for the Slice-Successive Overrelaxation Package.

Line 2, Spaces 21-30, IPRSOR, Integer

Printout interval. At the end of every IPRSOR iterations, the maximum head change between iterations will be printed. Thus, if IPRSOR is 3, the maximum head change between iterations will be printed at the end of the 3'rd, 6'th, 9'th, etc. iterations. If IPRSOR is set to 0 it will be changed to 999. The maximum head change is also printed at the end of each stress period regardless of the value of IPRSOR

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