An inverse formulation is developed for solving three-dimensional potential fluid flows which considers the magnitudes of the cartesian coordinates x, y, and z as the dependent variables in the space defined by the potential function and two mutually orthogonal stream surface functions whose intersection defines the physical space streamlines. This formulation reverses the usual role of the variables. In this inverse space irregular boundaries, with unknown position in the physical space, such as free surfaces become plane boundaries, and the space of most potential flow problems is a parallelepiped. The basin partial differential equations resulting from this formulation are nonlinear and three in number. Finite difference methods are developed for solving the space boundary value problems simultaneously, which are associated with these three equations. The applicability of the inverse formulation and the numerical solution is demonstrated by obtaining a solution to the three-dimensional, free surface flow past a vertical strut which extends through the fluid surface and is placed between channel walls.
Jeppson, Roland W., "Studies to Develop and Investigate an Inverse Formulation for Numerically Solving Three-dimensional Free Surface Potential Fluid Flows" (1972). Reports. Paper 303.