Characteristics in Evaluating Stream Functions in Ground-Water Flow

Abstract

In three-dimensional ground-water flow, two families of stream functions χ and λ are required to define ground-water flow. Recently, two partial differential equations that can be solved for spatial distributions of stream functions were developed. Solution of these partial differential equations of stream functions in ground-water flow with sinks/sources is practically impossible. The objective of this paper is to present the curve-tracing method that lends itself well to evaluating fields of stream functions in ground-water flow with or without sinks/sources. In the curve-tracing method, a characteristic curve of ordinary differential equations is constructed from a model-grid node to a Dirichlet boundary with prescribed spatial distribution of stream functions. Values of stream functions at the intersection of the characteristic curve and the Dirichlet boundary are the values of stream functions at the model-grid node. A three-dimensional ground-water flow in the aquifer beneath the Borden Landfill in Ontario, Canada, is considered to demonstrate how the curve-tracing method can be applied to evaluate fields of stream functions.