3.2. Constant-Head Boundary Conditions

Constant-head boundary conditions apply to features that both discharge water to and receive water from the groundwater system, such as rivers, regional flow, lakes, and reservoirs.

The equation for the discharge of water to or from constant-head nodes is shown below:

(3.1)\[q_{h}=\sum_{i=1}^{n} C_{hi}\,\bigl(H_{Bi}-H_i\bigr)\]

Where:

  • \(q_h\) = functional representation of groundwater discharge due to the constant-head boundary condition [L³T⁻¹],

  • \(C_{hi}\) = leakance factor at node i [L²T⁻¹],

  • \(H_{Bi}\) = boundary head for the node i [L],

  • \(H_i\) = computed hydraulic head for the node i [L], and

  • n = number of nodes [L⁰].

The leakance factor (\(C_{hi}\)) has a non-zero value at constant-head nodes and zero elsewhere, so discharge (\(q_{hi}\)) can be non-zero only at constant-head nodes. The \(C_{hi}\) value controls how quickly the computed head (\(H_i\)) at node i reaches the user-specified boundary head (\(H_{hi}\)). The \(C_{hi}\) equals the user-specified “Leakance” value in MINEDW. This value relates to the water source for the constant-head node, its distance from the constant-head node, and the hydraulic conductivity of the path from source water to the constant-head node, as shown below. The \(C_{hi}\) does not require high precision. Generally, \(C_{hi}\) must be large enough to produce sufficient discharge so \(H_{hi}\) approaches \(H_{Bi}\). However, \(C_{hi}\) must not cause model calculation problems (e.g., numerical instability). The default \(C_{hi}\) value is 1,000.

(3.2)\[C_{hi}=K\,\frac{A}{L}\]

Where:

  • K = hydraulic conductivity of material between constant-head node and water source [LT⁻¹],

  • A = area associated with node i perpendicular to flow from water source [L²], and

  • L = length from water source [L].