Solution of three-dimensional free boundary problems by variable interchange

Abstract

The three-dimensional problem of the seepage of fluid through a circular earth dam is solved to illustrate a new approach to more general free boundary problems. The method is based on Boadway's transformation in which the dependent variable, representing velocity potential, is interchanged with one of the independent space variables, which then becomes the new dependent variable to be computed. The need to determine the position of the whole of the free surface in the three-dimensional physical space is reduced to locating the position of the separation line on a fixed plane boundary in the transformed domain. An iterative algorithm approximates within each single loop both a finite-difference solution of the partial differential equation and the position of the separation line.