Second-order theory of shallow free-surface flow in porous media

Gedeon Dagan*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The general equations of shallow free-surface flow in porous media are formally derived by an expansion similar to Friedrichs' (4) theory of shallow water-waves. The same equations are derived in an alternative way by a process of matching of asymptotic expansions, the shallow-flow approximation being obtained rigorously as an inner expansion. The first term of the expansion satisfies the same equations as the usual Dupuit-Forcheimer equations; however, a second-order term is for the first time presented.

Original languageEnglish
Pages (from-to)517-526
Number of pages10
JournalQuarterly Journal of Mechanics and Applied Mathematics
Volume20
Issue number4
DOIs
StatePublished - 1967
Externally publishedYes

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