Documentation and Verification of VST2D: A Model for Simulating Transient, Variably Saturated, Coupled Water-Heat-Solute Transport in Heterogeneous, Anisotropic, 2-Dimensional, Ground-Water Systems with Variable Fluid Density

Water-Resources Investigations Report 2000-4105



This report describes a model for simulating transient, Variably Saturated, coupled water-heatsolute Transport in heterogeneous, anisotropic, 2-Dimensional, ground-water systems with variable fluid density (VST2D). VST2D was developed to help understand the effects of natural and anthropogenic factors on quantity and quality of variably saturated ground-water systems. The model solves simultaneously for one or more dependent variables (pressure, temperature, and concentration) at nodes in a horizontal or vertical mesh using a quasi-linearized general minimum residual method. This approach enhances computational speed beyond the speed of a sequential approach. Heterogeneous and anisotropic conditions are implemented locally using individual element property descriptions. This implementation allows local principal directions to differ among elements and from the global solution domain coordinates. Boundary conditions can include time-varying pressure head (or moisture content), heat, and/or concentration; fluxes distributed along domain boundaries and/or at internal node points; and/or convective moisture, heat, and solute fluxes along the domain boundaries; and/or unit hydraulic gradient along domain boundaries. Other model features include temperature and concentration dependent density (liquid and vapor) and viscosity, sorption and/or decay of a solute, and capability to determine moisture content beyond residual to zero. These features are described in the documentation together with development of the governing equations, application of the finite-element formulation (using the Galerkin approach), solution procedure, mass and energy balance considerations, input requirements, and output options.

The VST2D model was verified, and results included solutions for problems of water transport under isohaline and isothermal conditions, heat transport under isobaric and isohaline conditions, solute transport under isobaric and isothermal conditions, and coupled water-heat-solute transport. The first three problems considered in model verification were compared to either analytical or numerical solutions, whereas the coupled problem was compared to measured laboratory results for which no known analytic solutions or numerical models are available. The test results indicate the model is accurate and applicable for a wide range of conditions, including when water (liquid and vapor), heat (sensible and latent), and solute are coupled in ground-water systems. The cumulative residual errors for the coupled problem tested was less than 10–8 cubic centimeter per cubic centimeter, 10-5 moles per kilogram, and 102 calories per cubic meter for liquid water content, solute concentration and heat content, respectively. This model should be useful to hydrologists, engineers, and researchers interested in studying coupled processes associated with variably saturated transport in ground-water systems.

Suggested Citation

Friedel, M.J., 2001, Documentation and verification of VST2D; a model for simulating transient, Variably Saturated, coupled water-heat-solute Transport in heterogeneous, anisotropic 2-Dimensional, ground-water systems with variable fluid density: U.S. Geological Survey Water-Resources Investigations Report 00–4105, 124 p.,

Table of Contents

  • Abstract
  • Introduction
  • Theoretical Background
  • Numerical Methods
  • Model Documentation
  • Model Verification
  • Summary
  • References
  • Appendix 1. Elemental Matrix-Vector Representation for Water, Heat, and Solute Equations
  • Appendix 2. Input/Output for Finite-Element GRID Generator (GRID)
  • Appendix 3. Model Input Files in Case 1 Validation (Water Transport)
  • Appendix 4. Model Input File in Case 2 Validation (Heat Transport)
  • Appendix 5. Model Input File in Case 3 Validation (Solute Transport)
  • Appendix 6. Model Input File in Case 4 Validation (Coupled Water-Heat-Solute Transport)

Additional publication details

Publication type Report
Publication Subtype USGS Numbered Series
Title Documentation and verification of VST2D; a model for simulating transient, Variably Saturated, coupled water-heat-solute Transport in heterogeneous, anisotropic 2-Dimensional, ground-water systems with variable fluid density
Series title Water-Resources Investigations Report
Series number 2000-4105
DOI 10.3133/wri004105
Year Published 2001
Language English
Publisher U.S. Geological Survey
Publisher location Reston, VA
Contributing office(s) Illinois Water Science Center, Toxic Substances Hydrology Program
Description xiv, 124 p.
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