GEOS 5311 Lecture Notes: BoundaryConditions

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].4

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 interest5

– any errors in boundary specification will have minimal

effect

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Telescopic Mesh Refinement and Boundary Conditions

Figure 3: Telescopic mesh refinement as a means for defining

boundary conditions [risky, but commonly practiced; Andersonand 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):9

– 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].11

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 low-

permeability 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 upstream13

linkages/aquifer interaction)

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Modflow Head-DependentConditions

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River Package

• Inputs: riverbed elevation (RBOT), conductance (CRIV =KrLM

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 mass-

balance 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].17

Bibliography

18

Anderson, M. P., and W. W. Woessner, Applied Groundwater Modeling , Academic Press, SanDiego, 1992.

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