Mathematical models consist of a governing equation, boundary conditions, and initiial conditions. Boundary conditions are mathematical statements specifying the dependent variable (head) or the derivative of the dependent variable (flux) at the boundaries of the problem domain.

Correct selection of boundary conditions is a critical step in model design. In steady-state simulations, the boundaries largely determine the flow pattern. Boundary conditions influence transient solutions when the effects of the transient stress reach the boundary. In this case, the boundaries must be selected so that the simulated effect is realistic. Seeting boundary conditions is the step in model design that is most subject to serious error.

Quantitative modeling of a groundwater system entails the solution of a boundary value problem, a type of mathematical problem that has been extensively studied and has applications in many areas of science and technology. The flow of groundwater is described in the general case by partial differential equations. A groundwater problem is defined by establishing the appropriate boundary value problem; solving the problem involves solving the governing partial diffgerential equation in the flow domain while at the same time satisfying the specified boundary and initial conditions. In groundwater problems, the solution is usually expressed in terms of head (h); that is head is usually the dependent variable in the governing partial differential equation. The solution to a simple boundary value problem in groundwater flow is given in the appendix and serves as an example of a formal solution to this type of problem.

Good to have somethings in common with you, the modeler. I have read this "BOOK" for several times, and remember it talks about The water table as a boundary. It says because of the water table's importance in groundwater systems, in system models, treating the water table as a boundary in the various ways.
1. the water table is usually conceptualized as free-surface recharge boundary - either where recharge equals zero and the water table is a stream surface or where recharge equals a specified value and the water table is neither a potential surface nor a stream surface.
2. sometimes the water table acts as a discharge boundary, particularly where it is near land surface and thus is subject to losses by evaporation and transpiration. The discharge from the water table in this case is usually conceptualized as function of the depth of the water table below land surface - that is as a function of the water table altitude. Thus, in a model simulation, the water table is treated as a head-dependent flux boundary.
3. As discussed in teh preceding section, teh water table may also be treated as a specified-head boundary in unstressed steady-state models; that is the position of the water table is fixed as part of the problem definition.

The water table table differs from other boundaries is it acts as a source of sink of water in transient-state problems because its position is not fixed. Because the storage coefficient associated with unconfined/water table, storage is large, significant quantities of water are released from storage during a decline in the water table, and, likewise, significant quantities must be supplied for a rise in the water table to occur.

It discusses the importance of the water table in natural systems, and characteristics not common to other system boundaries, it may be simulated by boundary conditions that differ significantly from one another in their characteristics, the role of the water table in a specific problem requires special consideration, and its simulation requires particular care.