GGU-CONTAM-RW: Program concept

There are a number of numerical methods available for contaminant transport modelling:

• finite-element method,

• finite-difference method,

• particle tracking method (and in particular the random walk method).

The finite-element method is the most powerful of these, not only due to the flexible mesh design. This gives rise to the most basic question: why use particle tracking at all (here the random walk method in particular)? The reason is numerical dispersion, which is not related to physical dispersion. Numerical dispersion occurs where the finite-element method and the finite-difference method are used. The reason for numerical dispersion is the generally linear approximation approach within an element. Where the contaminant front is discrete, such an approach is no longer capable of precisely modelling this front. The contaminant front smears, an effect like physical dispersion and which is therefore known as numerical dispersion.

Particle tracking methods do not suffer from this problem. The particle tracking method is the simplest method. This method is incorporated in the GGU-2D-SSFLOW steady-state application in the shape of flow lines. The particle tracking method cannot consider either dispersion or diffusion effects. Only convection can be taken into consideration (movement of particles at groundwater speed). If, in addition, you wish to consider dispersion, diffusion, etc., the random walk method is generally used. The analytical solution of simple flow processes with contaminant transport leads to functions that correspond to a Gaussian distribution. This function can be modelled with a random generator if sufficient attempts are made. This mathematical effect is utilised by the random walk method (random path method). The method first assumes propagation at groundwater flow velocity. This underlying velocity is superimposed upon by a dispersion (diffusion) velocity, the direction of which is determined by a random generator integrated in the application. In order to model the Gaussian curve mentioned above adequately, it is no longer sufficient to simply consider one contaminant particle. Rather, a multitude of particles is started, and their courses recorded. This also has the result that the accuracy of the analyses increases with the number of started particles. Because of the integrated random generator, you will not get the same result for any two different runs.

For contaminant propagation modelling a flow field is required (velocity magnitude and direction). GGU-CONTAM-RW gets this data from a record (e.g. "plgw.da1") generated in a previous analysis using the GGU-2D-SSFLOW application. It is therefore necessary to load this file first after opening the program. The flow field contained in this file remains constant for subsequent analyses.

Also typical for the random walk method is that analyses must be based on a rectangular mesh. This requirement does not conform to the flexibility of the triangular elements used in FEM (GGU-2D-SSFLOW), which forms the basis of the flow data for modelling. GGU-CONTAM-RW solves this problem by placing a rectangular array over the whole FEM mesh. It is possible to edit the rectangular array subdivisions within broad limits. In this system of triangular mesh and rectangular array, you now define the initial concentrations and any contaminant sources. The definition of time-dependent changes, such as performed in GGU-CONTAM-FE by means of polygon courses, is not possible using the random walk method. Once the initial concentrations have been defined, you must still specify how many particles to start. The program then assigns each particle a corresponding partial concentration. Now, during analysis, the paths of the contaminant particles are traced, and the number of particles found in each rectangular cell counted for each time step. The summation of all partial concentrations within a cell then provides the total concentration that applies for that cell. These explanations demonstrate,

• that numerical dispersion cannot occur with this procedure,

• that the accuracy of the analysis is increased with the number of started particles,

• that the accuracy of contaminant distribution is not increased with the number of rectangular cells.

Because of the discrepancies between the triangular mesh and the rectangular array, the results from the rectangular cells are always converted to fit the triangular mesh. GGU-CONTAM-RW therefore generates two records:

• Record 1 ("plgw_ras.plw")
  contains all results from the rectangular array. So, during subsequent evaluation using the GGU-PLGW application, a rectangular triangle mesh is displayed.

• Record 2 ("plgw_fe.plw")
  contains the values from the rectangular array recalculated to fit the triangular mesh.

Besides the flow field, the GGU-CONTAM-RW program requires information on the initial contaminant distribution conditions at time t = 0. These so-called initial concentrations can be arbitrarily defined. If you do not define any values, the program will assume an initial concentration of "0" at all nodes.

Apart from the flow field, the "RW vertical.da1" file also includes the effective pore space n_eff, upon which steady-state modelling is based. This steady-state soil property (n_eff) cannot be edited in the GGU-CONTAM-RW application. If amendment of this value were allowed, the flow field would no longer correlate to the calculated potentials and the contaminant transport modelling would produce nonsensical results. However, you must enter the additional soil properties required for contaminant propagation modelling.

Besides additional soil properties the GGU-CONTAM-RW application also allows you to assign temporally constant concentration sources to individual nodes. Soil properties (contaminant transport modelling), as well as the allocation of initial concentrations and concentration sources to system nodes (so-called boundary values), can be saved in a separate file in order to make them available again for later analyses.

Generally, when modelling contaminant propagation in groundwater systems, a flood of result values is generated. The modelling results are saved in a file (generally "_ras.plw" and "_fe.plw") by GGU-CONTAM-RW. Contaminant propagation data cannot be evaluated using the GGU-CONTAM-RW program. The GGU-PLGW program is available for this purpose; it is described in a separate user-manual. For example, it is possible to evaluate the results using isolines, animations, sections or hydrographs.

The GGU-CONTAM-RW program is opened by conventional WINDOWS operations. The program is equipped with a large amount of error queries. Even highly nonsensical input will usually be detected by the program and an error message be displayed on the screen. Independently of this you should, for security reasons, intermittently save extensive input, if only to save renewed input in the case of a power cut.