2-D Saturated/Unsaturated Transport

A Finite-Element Simulation Model for Saturated-Unsaturated Fluid-Density-Dependent Ground-Water Flow with Energy Transport or Chemically Reactive Single-Species Solute Transport

SUTRA-ANE includes SUTRA (A Finite-Element Simulation Model for Saturated-Unsaturated Fluid-Density-Dependent Ground-Water Flow with Energy Transport or Chemically Reactive Single-Species Solute Transport), and a user-friendly interface for SUTRA integrated within the Argus Open Numerical Environments (Argus ONE).

Purpose and Scope

SUTRA is a computer program which simulates fluid movement and transport of either energy or dissolved substances in a subsurface environment. The model employs a two-dimensional hybrid finite-element and integrated finite-difference method to approximate the governing equations that describe the two interdependent processes that are simulated:

SUTRA enables the user to:

Set SUTRA control parameters with a user-friendly and simple dialog.

Define the problem domain and boundary conditions using GIS and intuitive drawing tools.

Assign physical properties using GIS and intuitive drawing tools.

Automatically mesh the problem domain and run SUTRA.

Visualize SUTRA results using Vector visualization tools on top of the problem domain.

Visualize SUTRA results using 3D visualization tools on top of the problem domain.
Argus ONE is a modeling environment which combines Conceptual Modeling, CAD, GIS, Database, Geostatistics, Automatic Grid and Mesh Generation, Mathematical Spreadsheet-like functions, Scriptable Import/Export, and Scientific Visualization tools within one comprehensive workplace.

Argus ONE's desktop is an intuitive metaphor of the engineer's working environment. Using tools from the tool palette, the user easily controls and manipulates data and objects by click-and-drag techniques. To allow for many different types of information, the workplace resembles a series of transparency sheets which allows the user to overlay the different information types. Formulae can be embedded, spreadsheet-like, into information parameters, vastly expanding the ways in which data can be manipulated.

Argus ONE allows the user to conveniently organize physical data, generate meshes and grids, link and assign data to the meshes and grids, export the data to any numerical model and visualize model results. The product integrates all of the pre- and post-processing tasks and tools required to solve the various aspects of a physical problem:
The interface is a Plug-In Extension (PIE) which automates SUTRA pre and post processing tasks within the Argus ONE workplace. Running a SUTRA simulation from within the Argus ONE workplace using SUTRA-ANE involves three main stages:


Starting a new SUTRA project or opening a previously saved one from within the Argus ONE workplace, automatically loads a SUTRA-ANE Dialog and Layers Structure:
All the input which is required for a SUTRA simulation is assigned and stored through the Dialog and the Layers Structure.


After the preprocessing stage is done, SUTRA simulation input data is exported and SUTRA is invoked from within the Argus ONE workplace. The original USGS SUTRA code (version 0690-2D) was modified and code modifications were made at two levels: (1) Input/Output modifications: due to pre and post processing requirements. (2) Modules modifications: to enable a user control of the unsaturated (UNSAT) and the time dependent boundary conditions (BCTIME) modules from the SUTRA-ANE user interface.

In the present release, UNSAT is completely controlled by SUTRA-ANE. BCTIME is to be supported when Argus ONE is to enable stress periods management. Compilation of SUTRA was performed using Microsoft FORTRAN PowerStation.

After a SUTRA simulation is successfully terminated, two types of output files are created: (1) Standard SUTRA output files of general preprocessing information as well as simulation results. (2) Modified SUTRA scattered data output files required for postprocessing.


The data created by a SUTRA simulation is imported into SUTRA-ANE data type layers within the Argus ONE workplace. This data may then be visualized and analyzed using the Argus ONE visualization tools. Argus ONE offers six analysis and visualization tools for postprocessing tasks. These tools are: 3-D surface, Vector Diagram, Color Diagram, Contour Diagram, Pathlines Diagram, Cross-section Diagram.

SUTRA Processes

Simulation using SUTRA is in two dimensions, although a three-dimensional quality is provided in that the thickness of the two-dimensional region in the third direction may vary from point to point. Simulation may be done in either the areal plane or in a cross-sectional view. The spatial coordinate system may be either Cartesian (x,y) or radial-cylindrical (r,z). Areal simulation is usually physically unrealistic for variable-density fluid problems.
Ground-water flow is simulated through numerical solution of a fluid mass balance equation. The ground-water system may be either saturated, or partly or completely unsaturated. Fluid density may be constant, or vary as a function of solute concentrations or fluid temperature.
SUTRA tracks the transport of either solute mass or energy in the flowing ground water through a unified equation which represents the transport of either solute or energy. Solute transport is simulated through numerical solution of a solute mass balance equation where solute concentration may affect fluid density. The single solute species may be transported conservatively, or it may undergo equilibrium sorption (through linear, Freundlich or Langmuir isotherms). In addition, the solute may be produced or decay through first- or zero-order processes.
Energy transport is simulated through numerical solution of an energy balance equation. The solid grains of the aquifer matrix and fluid are locally assumed to have equal temperature, and fluid density and viscosity may be affected by the temperature.
Almost all aquifer material, flow, and transport parameters may vary in value throughout the simulated region. Sources and boundary conditions of fluid, solute and energy may be specified to vary with time or may be constant.
SUTRA dispersion processes include diffusion and two types of fluid velocity-dependent dispersion. The standard dispersion model for isotropic media assumes direction-independent values of longitudinal and transverse dispersivity. A velocity-dependent dispersion process for anisotropic media is also provided and is introduced in the SUTRA documentation. This process assumes that longitudinal dispersivity varies depending on the angle between the flow direction and the principal axis of aquifer permeability when permeability is anisotropic.

Some SUTRA Applications

SUTRA may be employed in one- or two-dimensional analyses. Flow and transport simulation may be either steady-state which requires only a single solution step, or transient which requires a series of time steps in the numerical solution. Single-step steady-state solutions are usually not appropriate for non-linear problems with variable density, saturation, viscosity and non-linear sorption.
SUTRA flow simulation may be employed for areal and cross-sectional modeling of saturated ground-water flow systems, and unsaturated zone flow. Some aquifer tests may be analyzed with flow simulation. SUTRA solute transport simulation may be employed to model natural or man-induced chemical species transport including processes of solute sorption, production and decay. Such simulation may be used to analyze ground-water contaminant transport problems and aquifer restoration designs. SUTRA solute transport simulation may also be used for modeling variable density leachate movement, and for cross-sectional modeling of salt-water intrusion in aquifers at both near-well or regional scales with either dispersed or relatively sharp transition zones between fresh water and salt water. SUTRA energy transport simulation may be employed to model thermal regimes in aquifers, subsurface heat conduction, aquifer thermal energy storage systems, geothermal reservoirs, thermal pollution of aquifers, and natural hydrogeologic convection systems.

SUTRA Numerical Methods

SUTRA simulation is based on a hybridization of finite-element and integrated finite-difference methods employed in the framework of a method of weighted residuals. The method is robust and accurate when employed with proper spatial and temporal discretization. Standard finite-element approximations are employed only for terms in the balance equations which describe fluxes of fluid mass, solute mass and energy. All other non-flux terms are approximated with a finite-element mesh version of the integrated finite-difference methods. The hybrid method is the simplest and most economical approach which preserves the mathematical elegance and geometric flexibility of finite-element simulation, while taking advantage of finite-difference efficiency.
SUTRA employs a new method for calculation of fluid velocities. Fluid velocities, when calculated with standard finite-element methods for systems with variable fluid density, may display spurious numerically generated components within each element. These errors are due to fundamental numerical inconsistencies in spatial and temporal approximations for the pressure gradient and density-gravity terms which are involved in velocity calculation. Spurious velocities can significantly add to the dispersion of solute or energy. This false dispersion makes accurate simulation of all but systems with very low vertical concentration or temperature gradients impossible, even with fine vertical spatial discretization. Velocities as calculated in SUTRA, however, are based on a new, consistent, spatial and temporal discretization. The consistently-evaluated velocities allow stable and accurate transport simulation (even at steady state) for systems with large vertical gradients of concentration or temperature. An example of such a system that SUTRA successfully simulates is a cross-sectional regional model of a coastal aquifer wherein the transition zone between horizontally flowing fresh water and deep stagnant salt water is relatively narrow.
The time discretization used in SUTRA is based on a backwards finite-difference approximation for the time derivatives in the balance equations. Some non-linear coefficients are evaluated at the new time level of solution by projection, while others are evaluated at the previous time level for non-iterative solutions. All coefficients are evaluated at the new time level for iterative solutions.
The finite-element method allows the simulation of irregular regions with irregular internal discretization. This is made possible through use of quadrilateral elements with four corner nodes. Coefficients and properties of the system may vary in value throughout the mesh.
SUTRA includes an optional numerical method based on asymmetric finite-element weighting functions which results in "upstream weighting" of advective transport and unsaturated fluid flux terms. Although upstream weighting has typically been employed to achieve stable, non-oscillatory solutions to transport problems and unsaturated flow problems, the method is not recommended for general use as it merely changes the physical system being simulated by increasing the magnitude of the dispersion process. A practical use of the method is, however, to provide a simulation of the sharpest concentration of temperature variations possible with a given mesh. This is obtained by specifying a simulation with absolutely no physical diffusion or dispersion, and with 50% upstream weighting. The result may be interpreted as the solution with the minimum amount of dispersion possible for a stable result in the particular mesh in use.
In general simulation analyses of transport, upstream weighting is discouraged. The non-upstream methods are also provided by SUTRA, and are based on symmetric weighting functions. These methods are robust and accurate when the finite-element mesh is properly designed for a particular simulation, and are those which should be used for most transport simulations.

SUTRA as a Tool of Analyses

SUTRA will provide clear, accurate answers only to well-posed, well-defined, and well-discretized simulation problems. In less well-defined systems, SUTRA simulation can help visualize a conceptual model of the flow and transport regime, and can aid in deciding between various conceptual models. In such less well-defined systems, the simulation can help answer questions such as: Is the (inaccessible) aquifer boundary which is (probably) ten kilometers offshore either leaky or impermeable? How leaky? Does this boundary affect the primary analysis of onshore water supply?
SUTRA is not useful for making exact predictions of future responses of the typical hydrologic systems which are not well defined. Rather, SUTRA is useful for hypothesis testing and for helping to understand the physics of such a system. On the other hand, developing an understanding of a system based on simulation analysis can help make a set of worthwhile predictions which are predicted on uncertainty of both the physical model design and model parameter values. In particular, transport simulation which relies on large amounts of dispersion must be considered an uncertain basis for prediction, because of the highly idealized description inherent in the SUTRA dispersion process.
A simulation-based prediction made with certainty is often inappropriate, and an "if-then" prediction is more realistic. A reasonable type of result of SUTRA simulation analysis may thus be: "Based on the uncertainty in location and type of boundary condition A, and uncertainty in the distribution of values for parameters B and C, the following predictions are made. The extreme, but reasonable combination of A, B and C results in prediction X; the opposite reasonable extreme combination of A, B, and C results in prediction Y; the combination of best estimates of A, B, and C, results in prediction Z, and is considered most likely."
In some cases, the available real data on a system may be so poor that a simulation using SUTRA is so ambiguously defined that no prediction at all can be made. In this instance, the simulation may be used to point out the need for particular types of data collection. The model could be used to advantage in visualizing possible regimes of system behavior rather than to determine which is accurate.

SUTRA-ANE includes:


PC 486/Pentium with 16 MB RAM and Windows 3.x/95/ NT.

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Incredible NetworksΤελευταία Ενημέρωση 27 Ιουλίου 2004 - Last Revised on July 27, 2004
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