The plot on the left is at a regional scale, showing all elements in the model. The elements are in green. Head-specified linesinks form constant head boundaries at streams, ponds, and wetlands. A high conductivity glacial outwash valley aquifer is represented by a heterogeneity in the upper right area. A well with a U-shaped resistant (leaky) barrier is within this heterogeneity.

The plot on the right is the same model and solution as above, just a different, smaller window chosen for the plot. It shows the heterogeneity and barrier area in more detail.

The plot above is still the same model, but even more close up on the well and barrier. Note the accuracy of the solution near the well and barrier, despite the large extent of the entire model. This level of accuracy and flexibility with model boundaries is not found in finite-difference or finite-element numerical methods.

In this method, large numbers of analytic solutions are superpositioned to solve complex groundwater flow problems. The functions that are superpositioned are associated with particular aquifer features. Some of the functions contain parameters that are unknown when the problem is posed (for example, the discharge of a head-specified linesink). These unknowns are determined by specifying boundary conditions at control points located on or near the aquifer features (for example setting the head at the center of a head-specified linesink). The number of specified boundary conditions equals the number of unknown parameters, yielding a system of linear equations which is solved by standard methods. Once the unknown strengths are solved for, the resulting composite analytic solution satisfies the governing differential equation exactly except at singular points or lines associated with the analytic functions. The specified control point boundary conditions will be met exactly, and boundary conditions will be approximate between control points.

The aquifer modeled by TWODAN can consist of one or two hydraulically connected layers, it can be confined and/or unconfined, and it can be homogeneous or heterogeneous. Heterogeneities are input as closed polygon regions, each with a distinct set of aquifer properties (base elevation, lower layer K, lower layer thickness, upper layer K, and upper layer thickness). Heterogeneities can be nested inside one another and they can abut one another. See below a model of an aquifer with a variety of heterogeneities and mixed confined/unconfined conditions.

This plot shows three heterogeneities in a TWODAN model. Counting the outside aquifer, there are four zones, each with unique definitions of base elevation, upper and lower layer elevations, and upper and lower layer conductivities. The two larger ones that abut are more conductive and have lower base elevations than the regional aquifer outside. The small heterogeneity nested inside of the biggest heterogeneity has a conductivity much lower than its surroundings.

These features can have irregular shapes consisting of open or closed strings of line segments. The analytic implementation of these elements in TWODAN gives much greater accuracy than is possible with numerical methods. The discharge through resistant boundaries is proportional to a user-specified resistance (thickness/conductivity) and the head difference across the boundary. These elements offer an accurate way to model flow fields containing slurry walls, sheet-pile walls, etc. (see Fitts, C.R., Groundwater, 35(4), 1997). See models below using both the impermeable and resistant elements in remediation simulations.

The plot on the left shows two open-ended impermeable barriers in a simulation of a funnel and gate remediation. There is a high conductivity heterogeneity in the region to the left of the gate.

The plot on the right is of a closed, resistant boundary with a well pumping inside it. This type of remediation is sometimes used to isolate the contamination zone and reduce the amount of clean water pumped.

Solutions for both steady-state and transient wells are available. TWODAN is also capable of optimizing discharges of steady wells based on specified head and aquifer discharge conditions (see Fitts, C.R.,Groundwater, 32(4), 1994.). When transient wells are used, you can write an ASCII file listing head vs. time at a specified location; this file can be imported to a spreadsheet for plotting hydrographs.

Both discharge- and head-specified linesinks are implemented. Head-specified linesinks are typically used to represent constant-head boundaries. Discharge-specified linesinks can be used to model infiltration or pumping trenches.

Vertical infiltration or leakage to or from the aquifer can be modeled as uniform or as locally variable. Locally variable infiltration/leakage is modeled using solutions for circular area sources.

A uniform cross-flow in the aquifer can be input at any angle and discharge rate.

TWODAN Main Screen

Model Input Screen

Plot Settings Screen

Digitize using the mouse and a DXF basemap overlay. You can also digitize over the top of the previous plot showing contours, pathlines, etc. You can zoom or pan to a different view during the middle of a digitizing operations. You can continuously digitize multiple points, lines, or circles, quickly defining long barrier, heterogeneity, and constant-head boundaries. The digitized coordinates are temporarily stored in the Windows Clipboard. From there, the coordinates can be pasted into the TWODAN data grid or into other editor or spreadsheet files. As a bonus, you can use TWODAN as a general-purpose digitizing program with DXF basemaps.

Your plots can include any of the following: (1) Contours of head, potential, or stream function, (2) Pathlines can be traced upstream or downstream from single points, a series of points along a line, or a series of points around a circle (useful for defining the capture zone of a well). Arrows along pathlines are spaced at user-defined time intervals. (3) The DXF basemap. (4) A layout of model elements.

TWODAN plots can be output to a huge array of devices -- all those supported by the Windows operating system. Graphic plots may directed to the screen, Windows printer devices, bitmap (*.bmp) files, the clipboard, Surfer GRD files, or to DXF files. With all these options, it is now much easier to incorporate TWODAN graphic output into your reports. Printer plots may be scaled automatically to fit the page, or manually scaled to a specific scale (1 inch = 500 feet, for example). TWODAN automatically centers the plot on the page. You may print a plot with a landscape or portrait orientation, and you may add a border box and up to three lines of title text.

TWODAN labels contours automatically. You elect which contours to label (each contour, every other one, every fifth one, or every tenth one), and how frequently the labels occur along a given contour. Set these parameters once in the plot settings screen, and they will be used each time you press a button to make a plot.

The on-line Help is extensive and well-designed. The following forms of Help are available: tips that automatically display when you pause over a control, context-sensitive Help (F1 key), and Windows-standard detailed Help. The detailed Help is indexed, searchable, printable, and it contains embedded jumps to related topics.

Like many models, TWODAN will compile a list of target heads, model-calculated heads, and differences between these. In addition, TWODAN 5.0 has a very useful feature that plots the spatial distribution of the differences. See on the right an example of the graphic plotting of calibration results.

- Report-ready ASCII text output file summarizing the model inputs.
- Sum the aquifer discharge across a polyline. Digitize a multi-segment polyline, and TWODAN will calculate the discharge across this line. Handy for remediation design.
- Sum well or linesink discharges. Quickly sum the discharge of a wellfield or of a surface water defined by constant-head linesinks.
- Examine the analytic solution at a point. You digitize a point, and TWODAN calculates head, gradient, transmissivity, aquifer discharge, potential, and stream function at a point.
- Create a hydrograph of head vs. time at a point. Useful for models using transient well solutions. The output file is a comma-delimited list of head, time that can be imported into spreadsheet and other graphics programs for nice plotting.

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