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