To work effectively with GoPhast, several basic concepts must be
mastered. This section provides an introduction to those concepts
and tells where in this document more information about them may be
found.
PHAST uses finite-difference techniques for spatial and temporal discretization. A grid is required for spatial discretization. PHAST uses a point-distributed grid. The nodes in this grid are at the corners of elements (fig. 1A). Each node is surrounded by a cell that includes parts of one to eight elements (fig. 1B). Boundary and initial conditions are specified by node; aquifer properties are specified by element.
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A |
B |
Figure 1. The grid in PHAST. A. Nodes and a shaded element. B. Nodes and a shaded cell. (After Parkhurst and other, 2004). |
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In GoPhast, the grid can be at an angle to the global coordinate system. The coordinate system for the grid is aligned with the grid but has the same origin as the global coordinate system. The X and Y coordinates of the coordinate system of the grid are referred to as X’ and Y’ (X-Prime and Y-Prime). There is no Z’ because the grid is never rotated away from the horizontal plane. Coordinates values at the cursor location in both the global and grid coordinate system are displayed on the status bar. More information about the grid can be found in the PHAST documentation (Parkhurst and others, 2004).
GoPhast can be used to create the grid, rotate it, and add, move, or remove grid lines.
Data sets are used to represent distributed data in PHAST. Each data set represents an array of values. Because PHAST requires that some data be assigned to elements and other data be assigned to nodes, some data sets will have a value for each element and others will have a value for each node. One data set, the initial water table, is only defined for the top layer of nodes in the model. It is a two-dimensional (2D) data set. The remaining data sets are three-dimensional (3D).
In addition to the data sets used directly to represent input data for PHAST, the user can create additional data sets. The user-defined data sets can be used in “Formulas” to help define the distribution of values in the data sets that are used in PHAST. For more information on data sets, see “Data Sets Dialog Box” on page 38.
Formulas are used to help define the distribution of values in data sets. One simple example of a Formula would be just the name of another data set. For example, a valid formula for the Ky data set (which defines the hydraulic conductivity in the Y direction) would be “Kx”. (Kx is the data set that defines the hydraulic conductivity in the X direction.) Setting the formula for Ky to “Kx” would mean that in each element, the value of Ky would be same as the value of Kx in that same element.
Another simple example of a formula would be to set the formula for the Kz data set to “Kx/10”. This formula would mean that in each element, the value of Kz would be same as the value of Kx in that same element divided by 10. (Kz defines the hydraulic conductivity in the Z direction.)
These examples only hint at the power of formulas. In additional to simple arithmetic operations, it is possible to use mathematical functions such as “Sin” and “ln”. Geographic Information Systems (GIS) functions are also available in formulas as well as logic functions and functions related to the grid and objects.
For more information about formulas see “Formulas”, “Operators” “Functions”, and “Formula Editor Dialog Box” on pages 25, 27, 28, and 42 respectively.
“Objects” are points, lines and polygons drawn in the main window of GoPhast or imported from external files. Each object can have an upper and lower surface making it three dimensional (3D). For example, a polygon with an upper and lower surface is a solid. An object can also have a formula for just a single surface or it can have no surfaces. An object without any additional surfaces is two dimensional (2D). The surfaces associated with an object do not need to be flat. The surfaces are defined by formulas. The formulas allow the surfaces to have virtually any shape. There are some limitations; none of the line segments defining an object can cross one another, objects can not have holes in them, and there can only be, at most, one upper and one lower surface of the object.
Objects are used to set the values of data sets and boundary conditions by using formulas. Objects can set values in any of three ways. (1) Values can be interpolated among objects. (2) Objects can set the values of elements or cells whose centers or nodes are enclosed inside the object. (3) Objects can set the values of elements or cells intersected by the object. For the latter two methods, the order of the objects is important. Each object overwrites previous values so only the last value applied to an element or cell takes effect.
For more information about Objects see “Creating, Selecting, and Editing Objects in GoPhast” and “Object Properties Dialog Box” on pages 17 and 48 respectively.
Values are assigned to data sets at nodes or elements using the following procedure.
One way in which setting the values of a data set by interpolation can be useful is to specify the boundaries between geologic units. To do this, the user first creates a data set for each interface between adjacent geologic units. Then the user creates point objects to specify the elevations of the interfaces at known locations. Interpolation can then be used to specify the elevations throughout the grid. These data sets for the elevations can then be used in the formulas for the higher and lower surfaces of 3D Objects that define properties of aquifers.
The above procedure was followed in figure 2. First data points (black squares) were used to specify the top and bottom of a geologic unit by interpolation. Then polygons were used to define the value of the hydraulic conductivity of that unit. The colored cells represent the different values of hydraulic conductivity. Note the sloping surfaces of the geologic unit visible in the front and side view of the model.
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Figure 2. Example of 2D data sets used to define the top and bottom of a geologic unit. |
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