# Checks of Anaqsim

A series of Anaqsim models used to check the implementation of particular boundary elements, and where possible compare against either empirical relations or other software. Each input file associated with each model is provided and can be saved to a .anaq file and run within Anaqsim

- Check 1 - Uniform flow in a confined aquifer
- Check 2 - Uniform flow in a confined aquifer with uniform recharge
- Check 3 - Uniform flow in a confined aquifer with uniform leakage from below
- Check 4 - Uniform flow in an unconfined aquifer with uniform recharge
- Check 5 - Uniform flow in a confined interface aquifer with uniform recharge
- Check 6 - Uniform flow in an unconfined interface aquifer with uniform recharge
- Check 7 - Uniform flow in an unconfined aquifer with uniform recharge and two levels
- Check 8 - Uniform flow in a two-level confined aquifer system with circular opening connecting the two levels
- Check 9 - Transient simulation of the Theis (1935) solution
- Check 10 - Transient simulation of the Hantush (1967) analytic solution for mounding under a rectangular recharge area
- Check 11 - Comparison of complex multi-level Anaqsim model and equivalent MODFLOW 2005 model
- Check 12 - Check of Anaqsim drain line boundary
- Check 13 - Check of Anaqsim leaky barrier line boundary
- Check 14 - Uniform flow in a confined/unconfined aquifer with uniform recharge
- Check 15 - Uniform flow in a two-layer confined/unconfined aquifer with uniform recharge
- Check 16 - Head-dependent normal flux (3rd type) boundary
- Check 17 - Check of vertical leakage over polygon tool
- Check 18 - Multi-layer pumping test comparison with MLU
- Check 19 - 3D Pathline tracing comparison with MODFLOW

# Check 1 - Uniform flow in a confined aquifer

##### Checks confined domain, constant head line boundary, normal flux line boundary, pathlines.

In this single-

The model uses head-

The specific discharge, in accord with Darcy’s Law, is 0.06 and the average linear velocity is 0.30, which can be confirmed by moving the cursor around and examining the output.

The single pathline goes 1000 ft, and the arrowhead information indicates this takes 1000/0.3 = 3333 time units, as it should.

The aquifer discharge (specific discharge times saturated thickness) is 0.6, as it should be.

# Check 2 - Uniform flow in a confined aquifer with uniform recharge

##### Checks confined domain, constant head line boundary, normal flux line boundary, uniform recharge, 3D pathlines.

This is the same as check1, with the addition of uniform flux into the top of the domain (recharge) at a rate of 0.0005. Flow over the entire model is from left to right.

Over the 1000 unit distance from left to right, the uniform recharge adds an additional 0.50 to the domain discharge, which it does.

The domain discharge (specific discharge times saturated thickness) is about 0.35 at the left edge and about 0.85 at the right edge.

The one pathline starts at the left edge at the top of the domain. By the time it reaches the right side, recharge has added 0.50 units of discharge above the pathline, compared to 0.35 below it for a total domain discharge of 0.85.

At the right side, the fractional depth of the pathline is 0.5/0.85 = 0.59, as is should be, which places the pathline at an elevation of about 4.1 in the domain that goes from 0 to 10 elevation.

# Check 3 - Uniform flow in a confined aquifer with uniform leakage from below

##### Checks confined domain, constant head line boundary, normal flux line boundary, uniform leakage from below, 3D pathlines.

This is the same as check 2, but with the leakage coming from below and the pathline starting at the bottom of the aquifer on the left.

The discharges are the same as in check 2, but this time the pathline rises to a fractional depth of 0.41 at the right side (elevation 5.9), as it should.

# Check 4 - Uniform flow in an unconfined aquifer with uniform recharge

##### Checks unconfined domain, constant head line boundary, normal flux line boundary, uniform recharge, 3D pathlines

This is the same as check 2, but with an unconfined aquifer instead of a confined one. The base of the aquifer is at 0.

At the left edge of the model, the domain discharge is about 0.93. The recharge adds 0.50 as the pathline crosses the model from left to right, so the total discharge at the right side is 1.43.

The fractional discharge above the pathline at the right side of the model is 0.5/1.43 = 0.35, which puts it at about elevation 6.5.

Checking the specific discharge, average linear velocity and domain discharge anywhere in the model confirms consistency with Darcy’s Law.

# Check 5 - Uniform flow in a confined interface aquifer with uniform recharge

##### Checks confined interface domain, constant head line boundary, normal flux line boundary, uniform recharge, 3D pathlines

This is the same as check 2, but with a confined interface aquifer instead of a confined one. The top of of the domain is at –

The salt water elevation is 0.0 and the ratio of salt/fresh density is 1.025 (40:1 ratio of interface depth to head height).

At the left edge of the model, the head is 3.0 and at the right edge head is 0.3 (just above 0.25, the head where the interface would intersect the top of the domain and make it have zero saturated thickness). At the left side of the domain there is no interface, the domain is confined and the domain discharge is about 0.189.

For x > 450, the domain has an interface that rises near to the top of the domain at the right side of the model. At the right side, the head is 0.30, and the interface is at –

Checks of the interface and head at other points where the interface exists show this same ratio. The recharge adds 0.50 as the pathline crosses the model from left to right, so the total discharge increases to 0.689 at the right side, as it should.

The fractional discharge above the pathline at the right side of the model is 0.5/0.689 = 0.73.

Checking the specific discharge, average linear velocity, saturated thickness, head, and interface elevation anywhere shows that Darcy’s law and the Ghyben-

# Check 6 - Uniform flow in an unconfined interface aquifer with uniform recharge

##### Checks unconfined interface domain, constant head line boundary, normal flux line boundary, uniform recharge, 3D pathlines

This is the same as check 2, but with an unconfined interface aquifer instead of a confined one. The bottom of the domain is at –

At the left edge of the model, the head is 3.0 and at the right edge head is 0.1 (just above 0, the head where the domain would have zero saturated thickness). At the left side of the domain there is no interface, the domain is unconfined and the domain discharge is about 0.288.

For x > 402, the domain has an interface that rises near to sea level at the right side of the model. At the right side, the head is 0.10, and the interface is at –

Checks of the interface and head at other points where the interface exists show this same ratio. The recharge adds 0.50 as the pathline crosses the model from left to right, so the total discharge increases to 0.788 at the right side, as it should.

The fractional discharge above the pathline at the right side of the model is 0.5/0.788 = 0.63.

Checking the specific discharge, average linear velocity, saturated thickness, head, and interface elevation anywhere shows that Darcy’s law and the Ghyben-

# Check 7 - Uniform flow in an unconfined aquifer with uniform recharge and two levels

**Checks unconfined and confined domains, constant head line boundary, normal flux line boundary, spatially-**variable area sinks for leakage, 3D pathlines traced across multiple levels

This is the same as check 4, but with two model layers: an unconfined aquifer over a confined one. The base of the unconfined domain is at 5 and the confined domain goes from 0 to 5 elevation. A spatially-

The recharge adds 0.50 as the pathline crosses the model from left to right, so the total discharge at the right side is 0.78 + 0.16 + 0.50 = 1.44 (0.80 in the upper + 0.64 in the lower at the right side).

The pathline that started at the top of the upper level at the left side stays in the in the upper domain and its fractional depth in level 1 at the right side of the model is 0.5/0.80 = 0.62, which puts it at about elevation 6.95 = 5 + (1.0-

A second pathline starts at the left edge of the model in the middle of the upper level (elevation 17.5). At the left edge, 0.78/2 = 0.39 is the discharge above the pathline. When this pathline reaches the right edge of the model, there is 0.5 + 0.38 = 0.88 discharge above the pathline, which includes all of the upper level discharge (0.80) plus 0.08 in the lower level. The fractional depth of this pathline at the right side of the model is 0.08/0.64 =0.13 in the lower level level (elevation = 5 * (1.0 –

Checking the extraction along a line from 0, 500 to 1000, 500 shows a good approximation of the spatially-

# Check 8 - Uniform flow in a two-level confined aquifer system with circular opening connecting the two levels

##### Checks confined domains, constant head line boundary, normal flux line boundary, inter-domain boundaries with two levels transitioning to a single level

This is like Strack’s example 31.1, with uniform flow in the upper level far-

# Check 9 - Transient simulation of the Theis (1935) solution

**Checks confined domains, spatially-**variable area sinks for simulating storage changes

This is a single confined domain with K = 3, thickness of 10, T = 30, S = 0.001. One well pumps at a constant discharge. Initial heads are uniform at 100.

The simulation is transient with one 3-

Simulated hydrographs are generated at r = 2, 20, and 200. These are compared in the following figure to hydrographs computed from the Theis solution as programmed in the TWODAN software (listed as “Obs…” in the graph).

Checking the transient extraction along a line through the well indicates good approximation of the governing equation with this model. A plot of transient heads through the well is shown in the 2nd figure below.

Text file with Theis solution data: Check9_TheisData.txt

# Check 10 - Transient simulation of the Hantush (1967) analytic solution for mounding under a rectangular recharge area

##### Checks unconfined domains, spatially-variable area sinks for simulating storage changes and spatially-variable recharge, inter-domain boundary

This is an unconfined aquifer that is 6 m of saturated thickness. The rectangular recharge area starts adding recharge at a steady rate of 0.05 m/day at time zero. The recharge area is 60 m x 20 m. The aquifer horizontal K = 2 m/day and the specific yield is Sy = 0.12.

The Anaqsim simulation starts with heads = 0 (aquifer base = –

A hydrograph is generated at one of the corners of the recharge area, and this is compared to hand calculations of mounding at this point, computed with Equation 14 in the Hantush (1967) paper (Water Resources Research, 3(1), p. 227).

The results are as close as possible given the interpolation from tables required for the hand calculation. The Anaqsim generated head contours at t = 100 days is shown below with the recharge area outlined in green.