Invariant Imbedding and Unsteady Ground-Water Flow

by Shin Chang, Postgraduate Res. Engr.; Engrg. Systems Dept., Univ. of California, Los Angeles, CA,
William W-G Yeh, (A.M.ASCE), Assoc. Prof.; Engrg. Systems Dept., Univ. of California, Los Angeles, CA,

Serial Information: Journal of the Hydraulics Division, 1974, Vol. 100, Issue 10, Pg. 1343-1352

Document Type: Journal Paper


The invariant imbedding technique is used to find the unknown slope of the water table near the surface reservoir in a problem of unsteady ground-water flow into a surface reservoir in a large unconfined aquifer. The original nonlinear two-point boundary-value problem is transformed into an initial-value problem and an exact solution is obtained by the technique of quasilinearization. The invariant imbedding method involves no trial-and-error procedure and is easily programmed. This technique provides a useful tool in solving field problems and it becomes extremely powerful in solving a family of problems in which a set of unknown initial conditions are required to be determined from the corresponding given set of boundary conditions.

Subject Headings: Groundwater flow | Unsteady flow | Overland flow | Reservoirs | Slopes | Water table | Water flow | Aquifers

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