Chapter 4 Boundaries.

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Presentation transcript:

Chapter 4 Boundaries

4.1 Types of Boundaries Mathematical models consist of a governing equation, boundary conditions, and initial 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. The boundaries include: physical boundaries (an impermeable body of rock, a large body of surface water), hydraulic boundaries (groundwater divide, streamlines) .

Hydrogeological boundaries are represented by the following three types of mathematical conditions: Type 1. Specified head boundaries (Dirichlet conditions) for which head is given. Type 2. Specified flow boundaries (Neumann conditions) for which the derivative of head (flux) across the boundary is given. Type 3. Head-dependent flow boundaries (Cauchy or mixed boundary conditions) for which flux across the boundary is calculated given a boundary head value.

4.2 Setting Boundaries Surface water bodies that fully penetrate the aquifer form ideal specified head boundaries. Termination of an aquifer at an impermeable rock unit forms a convenient physical no-flow boundary. Some fault zones also forms ideal no-flow boundaries.

4.3 Simulating Boundaries (1) Specified head: A specified head boundary is simulated by setting the head at the relevant boundary nodes equal to known head values. (2) Specified flow: Specified flow conditions are used to describe fluxes to surface water bodies, spring flow, under flow, and seepage to or from bedrock underlying the modeled system. Whenever possible, specified head conditions are selected over specified flow, however, because it is easier to measure head than to measure flow.