GEOS 5311 Lecture Notes: Boundary
Conditions
Dr. T. Brikowski
Spring 2013
Vers. 1.14, March 31, 2010
Introduction
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Why Boundaries?
Figure 1: Boundaries control your domain! Often a model just
determines how water moves from one boundary to another.
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Boundary Classifications
• Real world
– Physical boundary (sharp change in hydraulic conductivity)
– Hydraulic boundary (groundwater divides, streamlines)
• Mathematical Model
– Fixed head (Dirichlet)
– Fixed flux (Neumann)
– Head-dependent flux (mixed, Robbins or 3rd kind)
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Natural Boundary Types
Figure 2: Example of natural physical and hydrologic boundary
types [Anderson and Woessner , 1992, Fig. 4.4].
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Selecting Boundaries
• Physical or Natural Boundaries (Fig. 2)
– geologic contacts, margins of surface water bodies, etc.
• Hydraulic Boundaries
– water divides or streamlines
– derived from conceptual model (risky) or larger-scale
models (telescopic mesh refinement)
– really only useful in steady-state problems. Streamlines
often move in transient problems
• Distant Boundaries
– when in doubt, put boundaries far from area of interest
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– any errors in boundary specification will have minimal
effect
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Telescopic Mesh Refinement and Boundary Condition
Figure 3: Telescopic mesh refinement as a means for defining
boundary conditions [risky, but commonly practiced; Anderson
and Woessner , 1992, Fig. 4.5].
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Detailed Description
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Specified Head (Dirichlet)
• Conceptually this is an infinite source or sink for water
• usually represents a body of surface water
• accurate only when the unmodeled flux (i.e. whatever
external flux maintains the body’s water level) exceeds the
modeled flux by a factor of 10 or more
• good to have at least one of these to provide a reference
point for modeled head
• error-prone on coarse grids
• Modflow (Fig. 4):
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– IBOUND array (*.ba6 file) set to negative value, head
value specified in starting head array (*.ba6 file)
– use General Head Boundary Package for variable but
externally-controlled head boundary (usually a variable lake
level, etc.)
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Modflow Boundary Conditions
Figure 4: Boundary condition specification in Modflow. Note areal fluxes
(e.g. recharge) are converted to volumetric by multiplying by cell surface
area [Anderson and Woessner , 1992, Fig. 4.6].
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Specified Flux (Neumann)
• use when water exchange with surface water bodies is
independently known (e.g. through geochemical studies)
• most accurate type of boundary condition (i.e. good to use
since won’t accidentally generate infinite fluxes)
• Modflow:
– implement non-zero flux using Well (“placing” water into
the boundary cell for known volume of flux) or Recharge
Package (for known Darcy velocity)
– no-flow boundaries are the default along model edge
and between inactive (IBOUND=0) and active cells (i.e.
conductance of that cell face is set to zero)
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Head-Dependent Flux
• usually a leakage process, e.g. from a lake through lowpermeability fine sediments below
• Modflow:
– River Package
∗ vertical leakage through basal sediments
∗ user specifies bottom elevation of riverbed and vertical
conductance
∗ each river cell can serve as source or sink
– Drain Package: same as river except no interaction if
h < zdrain (elevation of drain bottom)
– Stream Package: same as river, but accounts for
surface flow routing (river stage depends on upstream
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linkages/aquifer interaction)
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Modflow Head-Dependent
Conditions
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River Package
• Inputs: riverbed elevation (RBOT), conductance (CRIV =
Kr LM
M ), stage (HRIV, height above RBOT)
• note conductance calculated from riverbed hydraulic
conductivity (Kr ), width W , and cross-sectional area (L·W )
• depends on head difference between river and its base
(perched stream) or head in the aquifer (cell head ≥ HRIV
• note Stream package simply adds a calculated discharge
based on Manning Equation1, and maintaining a water massbalance in the stream/river in the downstream direction
1
../../../../Hydrogeology/LectureNotes/Streamflow/Streamflow_
Measurement.html
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Input for River Package
Figure 5: Boundary condition specification in Modflow. Note areal fluxes
(e.g. recharge) are converted to volumetric by multiplying by cell surface
area [Anderson and Woessner , 1992, Box 4.1, Fig. 1].
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Bibliography
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Anderson, M. P., and W. W. Woessner, Applied Groundwater Modeling, Academic Press, San
Diego, 1992.