Inverse Solution to Three-Dimensional Flows

by Roland W. Jeppson, Assoc. Prof. of Civ. Engrg.; Utah State Univ., Logan, UT,

Serial Information: Journal of the Engineering Mechanics Division, 1972, Vol. 98, Issue 4, Pg. 789-812

Document Type: Journal Paper


Methods are developed for obtaining numerical solutions to three-dimensional, inviscid, incompressible fluid flows and free surface Darcian flows in porous media. An inverse formulation is used which considers the magnitudes of the cartesian coordinates as the dependent variables, and utilizes the potential function and two mutually orthogonal stream functions whose intersections define the streamlines of the flow as the independent variables. In this inverse space irregular boundaries and phreatic surfaces whose positions are unknown a priori in the physical space, become planes of known positions and, consequently, the region of the partial differential equations boundary value problem is defined. This special boundary value problem is solved by utilizing finite differences. The applicability of the methods are demonstrated by implementing them in a computer program and obtaining a solution to three dimensional Darcian seepage flow through a dam with a drain over a portion of the base of the toe.

Subject Headings: Three-dimensional flow | Fluid flow | Porous media flow | Numerical methods | Free flow | Water table | Boundary value problem | Free surfaces

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