Variational Approach to Non-Darcy Flow

by John A. McCorquodale, (A.M.ASCE), Asst. Prof.; Dept. of Civ. Engrg., Univ. of Windsor, Windsor, Ontario, Canada,

Serial Information: Journal of the Hydraulics Division, 1970, Vol. 96, Issue 11, Pg. 2265-2278

Document Type: Journal Paper


The principles of variational calculus are applied to solve the nonlinear partial differential equation for steady and unsteady unconfined non-Darcy flow through porous media. A functional is proposed which will yield solutions for the laminar, transitional and turbulent flow regimes. The solution represents the minimization of the rate of energy dissipation with enforced flow continuity. A finite element scheme is used to obtain the minimizing field. Examples of the method applied to steady and unsteady free surface flow is described in a rectangular rockfill section. The finite element and experimental flow fields are in good agreement.

Subject Headings: Porous media flow | Unsteady flow | Turbulent flow | Finite element method | Differential equations | Laminar flow | Energy dissipation | Free surfaces

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