Initial And Boundary Conditions

The most common types of boundary conditions are Dirichlet, Neumann, and Cauchy.

1. Dirichlet conditions occur when a portion of the boundary is at a prescribed head level. For example, if an aquifer is adjacent to a stream or lake, then h(x,y, t) = /j(x, y, t) (x, e 9Qt

where/j is a known function and 9ilj is the boundary.

2. Neumann conditions occur when a portion of the boundary has a specified flow transversing it normal to the boundary. For example, if a portion of the aquifer boundary is subject to recharge, then

where f2 is a known function and dh/dn is the normal derivative to the boundary 9il2-

3. The Cauchy, or mixed boundary, condition occurs when both the head and its normal derivative are specified on the boundary 9fi3, for example, the induced infiltration in a coupled aquifer and stream system (Prickett and Lonnquist, 1971).

Prior to solving the groundwater flow equation, the initial condition must be specified in the flow domain.

Typically, the initial condition can be expressed by h(x,y,Q)=Mx,y) (x,y)eQ (21)

where Q is the flow domain and f3 is a known function.

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