PUBLICATIONS - Report, "Direct solution algorithm for the two dimensional ground-water flow model,"




             UNITED STATES DEPARTMENT OF THE INTERIOR
                        GEOLOGICAL SURVEY
                        RESTON VIRGINIA  22092

                                                  Code 4351 5016
                                             Ground Water Branch

                                                  May 21, 1979

GROUND WATER BRANCH TECHNICAL MEMORANDUM NO. 79.10

SUBJECT:  PUBLICATIONS - Report, "Direct solution algorithm for
                         the two dimensional ground-water flow
                         model," by S. P. Larson, Open-file report
                         79-202

Finite-difference approximations of the differential equation of
ground-water flow result in a system of simultaneous equations to
be solved.  Iterative methods such as the iterative alternating-
direction implicit procedure and the strongly implicit procedure
have been used to solve these equations in the WRD ground-water
flow models since the early 1970's.  Iterative techniques have
been used to the exclusion of direct methods because of the higher
computer storage and computational work effort of the latter.
Recent work has shown that use of a scheme for ordering node
points, called D4 ordering, can result in a significant saving in
the computational effort required to solve the system of equations
using a direct solution.

Steve Larson has made comparisons of performance of the D4 method
with the strongly implicit procedure, line-successive
overrelaxation, and the ierative alternating-direction implicit
procedure.  These comparisons indicate that the D4 method can be
more effective solution technique for steady-state problems
involving up to about 3,000 gridpoints.  Larson suggests that for
two-dimensional transient problems involving large time steps D4
may be similarly more effective for certain types of problems for
which iterative methods currently are used.

The report, a copy of which is enclosed, contains a FORTRAN
computer code that is compatible with the WRD two-dimensional
ground-water flow model and indicates the changes necessary to
implement the D4 subroutine.

Limited additional copies of the report are available upon request
to the Ground Water Branch.



                              (s) Charles A. Appel
                              (for) Gerald Meyer
                              Chief, Ground Water Branch

Enclosure

WRD Distribution:
     A (memo only)
     B
     FO-LS
     SL (memo only)