Dynamic Time-Variable Boundary Conditions
Jirka Simunek
This series of examples demonstrate the use of Dynamic Time-Variable Boundary Conditions.

Dike1:
Flow through a dike with a time-variable pressure head boundary condition on the left side
(Kode = 3; blue color), seepage face (Kode=-2, dark green) on the right side, and atmosphericboundary condition (Kode=-4; light green) on the top. The dike is 70 cm high and 200 cm wideat the bottom. The time-variable pressure head BC on the right represents the fluctuating waterlevel in the upstream reservoir.

Specified pressure heads are linearly interpolated in time, so that there are no sudden changes inwater levels. The specified pressure head (hBnd) is applied to the lowest located node (i.e., thenode with the lowest z-coordinate, zBot) with the applied time-variable boundary condition. The
applied pressure head in other nodes is recalculated, taking into account the vertical location of aparticular node (i.e., h=hBnd-(z-zBot)). Therefore the node located at the water level in thereservoir will have zero applied pressure head. Calculated pressure heads for nodes above thewater level are negative, which is not realistic. HYDRUS offers several ways how to deal withthese nodes. User can select that instead of the time-variable boundary condition, these nodes(i.e., above the water level) will have either a) zero flux, b) atmospheric BC, or c) seepage face.
In this example, we use option (b) with the atmospheric BC. This means that applied
atmospheric fluxes (precipitation and evaporation) will be applied to nodes that are above thewater level.
Note that the length of the potential seepage face (specified by a user) should reflect as closely as
possible the length of the actual seepage face (calculated by the program), since one can not use
the option “Apply atmospheric boundary conditions to nonactive seepage face”. This is becauseonly one (other than interpolation) “Boundary Conditions Options for Time-Variable Head” canbe used. The nonactive part of the seepage face will thus have a no flow boundary condition
applied.

Observation N odes: Pressure H eads
4030
20
100

N1-10

N2-20

N3-30

N4-40
0

510152025

Time [day s ]This figure shows pressure heads at four observation nodes. The N1 node is the left-most node,
which shows the applied time-variable pressure head specified at this node. Notice the linear
interpolation of pressure head values.

2A ll N on-A tmospheric Fluxes
200
100
0-100-200-300-400-500-600
0510152025

Time [day s ]This figure shows non-atmospheric boundary fluxes. While the black line represents the inflow
across the time-variable pressure head boundary, the green line represents the outflow across theseepage face. Notice smooth changes in fluxes at both boundaries as a result of smooth changes
of applied pressures. There is rainfall between 10 and 15 d, which leads to more abrupt changes
in fluxes at these times.

This figure shows the pressure head profile at the end of the simulation. Notice that the line
between yellow and orange colors represents the ground water level. The cross-section of thisline with the seepage face boundary defines the active and nonactive parts of the seepage face.

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Dike2:
Flow through a dike with two time-variable pressure head boundary conditions (on both sides,
Kode=3 on the left and Kode=7 on the right; blue color) and the atmospheric boundary condition(Kode=4; light blue) on the top.

Notice that interpolation in time can be applied to only one time-variable pressure head boundary(Kode=3).

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Observation N odes: Pressure H eads
4030
20

N110

N20

N3-10

N4-20

N5-30
-40
0

510

152025Time [day s ]This figure shows pressure heads at five observation nodes. The N1 node (black line) is the leftmost node, which shows the applied time-variable pressure head specified at this node. Noticethe linear interpolation of pressure head values. The N2 node (blue line) is the right-most node,
which also shows the applied time-variable pressure head specified at this node. However, noticethat here pressure heads were not interpolated with time. This has quite significant effects onboundary fluxes.
A ll N on-A tmospheric Fluxes

A ll B oundaries

400600

300

400

200

200

10000-200-100-400-200-600

-300

-800
0

5101520250

Time [day s ]510152025

Time [day s ]This figure shows non-atmospheric boundary fluxes (actual on the left and cumulative on theright). While the black line represents the inflow (outflow, when values are positive) during
rainfall between 10 and 15 days) across the time-variable pressure head boundary (Kode=3), thepink line represents the outflow across the seepage face. Notice smooth changes in black line,reflecting gradual changes in pressure heads at this boundary (Kode=3), and large peaks in pinkline, reflecting sudden changes in pressure heads at this boundary (Kode=7). However, noticethat since these peaks are relatively short, they do not have a large effect on the cumulative
fluxes. Both fluxes (actual and cumulative) are in cm2, which is in fact cm3 per 1 cm in theperpendicular (y) direction.

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