This section describes methods for handling two-dimensional groundwater flow problems including superposition, the method of images, and the potential and flow function.
The differential equation for two-dimensional steady flow in a homogeneous aquifer is
Because this equation is a linear and homogeneous differential equation, the principle of superposition applies. The principle states that if two different functions $1 and $2 are solutions of Laplace's equation, then the function
is also a solution.
Superposition of solutions is valuable in several groundwater problems. For example, the case of groundwater flow due to simultaneous pumping from several wells can be solved by the superposition of the elementary solution for a single well.
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