Introduction to VAM2D
VAM2D (Variably-Saturated Analysis Model in Two (2) Dimensions) is a two-dimensional (2-D) finite-element model that simulates transient or steady-state groundwater flow and contaminant transport in porous media. VAM2D analyzes unconfined flow problems using a rigorous saturated-unsaturated modeling approach using efficient numerical techniques. Accurate mass balance is maintained even when simulating highly nonlinear soil moisture relations. Hysteresis effects in the water retention curve can also be simulated. A wide range of boundary conditions can be treated including seepage faces, water table conditions, recharge, infiltration, evapotranspiration, and pumping and injection wells. The contaminant transport option can account for advection, hydrodynamic dispersion, equilibrium sorption, and first-order degradation. Transport of a single species or multiple parent-daughter components of a decay chain can be simulated. The code can perform simulations using an areal plane, cross section, or axisymmetric configuration. An independent review of flow and transport computer codes conducted for the U.S. NRC (Kozak et al., 1989) states about VAM2D: "It is easy to use, is robust and has a wide range of numerical stability."
VAM2D Methods of Analysis
Groundwater resource investigations. VAM2D can be used to simulate groundwater flow in confined or unconfined aquifers as well as moisture and solute movement in unsaturated zones.
Groundwater contamination investigations. VAM2D can predict contaminant plume extent and rate of migration to aid in the design of monitoring programs and remedial schemes.
Nuclear waste subsurface performance assessment. VAM2D can be used to simulate water flow in the unsaturated zone surrounding a repository and perform risk assessment for potential radionuclide migration.
The saturated-unsaturated flow equation in VAM2D is solved using the Galerkin method with either Picard or Newton-Raphson iterative schemes to treat nonlinearities. The use of the upstream weighted residual finite-element method is used to solve the advective-dispersive transport equation. This circumvents numerical oscillation problems. Matrix solutions of the flow and transport problems are performed using efficient iterative solvers based on the preconditioned conjugate gradient and ORTHOMIN methods for symmetric and a nonsymmetric matrices, respectively.
VAM2D Simulation Options
Coordinate Systems and Grid Configurations
The input of VAM2D has been structured to simplify defining the problem for the computer. Cartesian coordinate systems in an areal (x-y) plane and a vertical (x-z) plane as well as an axisymmetric cylindrical coordinate (r-z) system are available. The model region is divided into a number of rectangular and/or orthogonal curvilinear elements. Such elements are simple to deal with and their matrices can be easily computed using efficient influence-coefficient formulas. Furthermore, regions with irregular boundary geometry can be accurately represented. When a rectangular grid is used, VAM2D allows the grid to be inclined at any angle to accommodate sloping formulations (e.g., hill-slope problems). The code also allows the user to obtain a stepped approximation of irregular boundaries and lateral discontinuities by blocking out unwanted elements in the grid.
Heterogeneous and anisotropic material properties may be included in flow and transport analyses. Layering, discontinuities, and other heterogeneities can be treated. For a variably-saturated flow analysis, soil moisture relations are supplied to the code in functional form using the well known Brooks-Corey and Mualem van Genuchten relations with extensions to handle hysteresis. For transport analysis, velocity-dependent dispersion, moisture-dependent retardation, sorption, and decay are permitted.
Boundary condition input in VAM2D for water flow simulations may be in terms of prescribed nodal values of head or prescribed integrated nodal fluid flux values. In a variably saturated flow analysis, the code can accommodate seepage faces, infiltration or evaporation, and plant root extraction. For simulations of deep soil profiles, the lower boundary condition can be set to approximate a free draining soil with zero vertical pressure head gradient. Boundary conditions for flow may be either constant in time or variable with either stepwise or continuous changes.
Boundary condition inputs for solute transport simulations in VAM2D may be prescribed nodal values of concentration or prescribed integrated nodal values of solute mass fluxes. Solute concentration or flux values at the boundaries can be either constant in time or variable in time with either continuous or stepwise changes. An additional option is available for modeling conditions in which source concentrations exhibit first-order decay.
Output of flow analyses in VAM2D include nodal values of hydraulic or pressure head, Darcy velocities and saturation values. This output may be printed at specified intervals or time values. A printout option that provides relationships of simulated head versus time is also available for user-specified observation points. Output of solute transport analyses are nodal values of concentration and solute fluxes. For specified nodes, the relationships of concentration versus time (breakthrough curves) can also be provided. Complete flow and transport mass balances may be provided. To facilitate postprocessing using a wide variety of commercial data analysis and graphical software, the model output can be written in a general x,y,z column format.
VMPLOT provides postprocessing for VAM2D flow and transport simulations. Using VMPLOT, you can generate the following:
Code Testing and Model Validation in VAM2D
Plots of the model grid
Plots of different material regions
Contour plots of saturation, hydraulic head, pressure head, and concentration
Vector plots of the groundwater flow velocity field
Plots of the fluxes crossing boundaries
Plots of the water-table position
The model formulation used in VAM2D is a descendant of the formulation used in the SATURN code presented by Huyakorn et al. (1984, 1985). VAM2D has continued to be enhanced - the published algorithms and their coding to achieve greater flexibility, wider capability, and more robust numerical performances when dealing with difficult cases. The VAM2D code has been checked for numerical accuracy against several alternative analytical and numerical codes including FEMWATER/FEMWASTE and UNSAT2. The code has been applied to a wide variety of field problems (e.g., McCord et al., 1988; Kool et al., 1990) which have demonstrated its utility and versatility.
The application of VAM2D has been documented in the following studies.
Huyakorn, P.S. et al., 1984. Techniques for Making Finite Element Competitive in Modeling Flow in Variably-Saturated Porous Media, Water Resour. Res., 20, 8, 1099-1115.
Huyakorn, P.S. et al., 1985. Finite Element Matrix and Mass Balance Computational Schemes for Transport in Variably-Saturated Porous Media, Water Resour. Res., 21, 3, 346-358.
McCord, J.T. et al., 1988. Field Experiments and Numerical Simulations of Unsaturated Flow and Transport, Proc. of NATO Advanced Study Institute on Recent Advances in Modeling Hydrologic Studies, Sintra, Portugal, July 9 - 23.
Kool, J.B. et al., 1990. Model Calibration and Simulation of Flow in a Heterogeneous Soil, Proc. of Intern. Conference on Calibration and Reliability in Groundwater Modeling. IAHS Publication No. 195, pp. 321-330.
Kozak, M.W., M.S.Y. Chu, C.P. Harlan, 1989. Background Information for the Development of a Low-Level Waste Performance Assessment Methodology, U.S. Nuclear Regulatory Commission, Washington, D.C., NUREG/CR-5453, SAND89-2509, Vol. 4.
Pentium with 8 MB RAM, and HP PostScript or compatible printer for VMPLOT.