American Society of Civil Engineers

The Hopscotch Algorithm for Three-Dimensional Simulation

by Geneviève Ségol, A.M.ASCE, (Proj. Engr., Bechtel Nat. Inc.,50 Beale St., San Francisco, CA 94105)

Journal of Hydraulic Engineering, Vol. 118, No. 3, March 1992, pp. 385-406, (doi:

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Document type: Journal Paper
Abstract: This paper presents results obtained for the solution of the three-dimensional ground-water flow and mass-transport equations using the Hopscotch algorithm, an iterative technique that alternates explicit and implicit finite difference approximations of the governing equations. While the method is not new, it has been mostly ignored, particularly in three dimensions. Three application examples are presented: (1) Contaminant transport in a hypothetical, steady-state, saturated ground-water flow system; (2) infiltration of a solute in an unsaturated soil; and (3) advection and advection-diffusion of a Gaussian hill in rotational flow fields. The results indicate that the Hopscotch algorithm is an intriguing and powerful alternative to SIP, SOR, and conjugate gradient techniques in three dimensions. Certainly it warrants more research.

ASCE Subject Headings:
Finite difference method
Groundwater flow
Mass transport
Numerical models
Three-dimensional models