Methods are developed and defined for obtaining numerical solutions to three-dimensional, free surface, invisvid, incompressible fluid flows and three-dimensional free surface Darcian flow in porous media. Since those boundaries consisting of free surface are unknown a priori, a solution to the space boundary value problem resulting from a formulation in the physical space is very difficult, if not impossible, to obtain. Consequently, the methods described herein are based on a formulation in a space defined by a potential function and two mutually orthogonal stream surfaces whose intersections define the streamlines of the flow. In this space the positions of free surfaces are known. The formulation considers the magnitudes of the Cartesian coordinates x,y, and z as the dependent variables. The applicability of the methods are demonstrated by implementing them in a computer program and by obtaining solutions to four problems with slightly different geometries of three-dimensional Darvian seepage flow of water through a dam with a drain over only a portion of the toe. Isometric drawing of the space flownets display the results from these solutions. Also a number of regular flownets are given which were constructed by projecting the points of intersection of the two stream surfaces and/or equipotential surfaces onto horizontal or vertical planes.
Jeppson, Roland W., "Inverse Solutions to Three-Dimensional Free Surface Potential Flows" (1971). Reports. Paper 306.