1. General Model Information

Name: Simulating the Two-Dimensional Movement of Water, Heat, and Multiple Solutes in Variably-Saturated Porous Media

Acronym: CHAIN2D

Main medium: terrestrial
Main subject: hydrology
Organization level: ecosystem
Type of model: partial differential equations (finite elements,2D), ordinary differential equations
Main application:
Keywords: water flow, solute transport, unsaturated, porous media, hysteresis, saturated, equilibrium adsorption, solute transport, zero-order production, first order degradation, water uptake, solute uptake, heat conduction, convection,Richards equation , convection-dispersion equation, sink terms, Garlekin finite element numerics


Simunek, J.
U. S. Salinity Laboratory, USDA, ARS
450 West Big Springs Road
Riverside, CA 92507-4617

Walter Russell
U.S. Salinity Laboratory
450 West Big Springs Road
Riverside, CA 92507-4716Tel: 909-369-4850
FAX: 909-342-4964
email: wrussell@ussl.ars.usda.gov


Simunek. J., van Genuchten M.Th.U.S. Salinity Laboratory, USDA, ARS, Riverside, California.


CHAIN_2D is a model for simulating two-dimensional variably saturated water flow, heat transport, and the movement of solutes involved in sequential first-order decay reactions. The program numerically solves the Richards' equation for saturated-unsaturated water flow and the convection-dispersion equation for solute and heat transport. The flow equation incorporates a sink term to account for water uptake by plant roots. The water flow part of the model can deal with prescribed head, gradient, and flux boundaries, as well as boundaries controlled by atmospheric conditions. Free drainage boundary condition and a simplified representation of nodal drains using results of electric analog experiments is also included. The heat transport equation considers transport due to conduction and convection with flowing water. The solute transport equations consider convective-dispersive transport in the liquid phase, as well as diffusion in the gaseous phase. The transport equation includes provisions for nonlinear nonequilibrium reactions between the solid and the liquid phases, linear equilibrium reactions between the liquid and gaseous phases, zero-order production, and two first-order degradation reactions: one which is independent of other solutes,and one which provides the coupling between solutes involved in the sequential first-order decay reactions.
The program may be used to analyze water and solute movement in unsaturated, partially saturated, or fully saturated porous media. CHAIN_2D can handle flow regions delineated by irregular boundaries. The flow region itself may be composed of nonuniform soils having an arbitrary degree of local anisotropy. Flow and transport can occur in the vertical plane, the horizontal plane, or in a three-dimensional region exhibiting radial symmetry about the axis.
The governing flow and transport equations are solved numerically using Galerkin-type linear finite element schemes. Depending upon the size of the problem, the matrix equations resulting from discretization of the governing equations are solved using either Gaussian elimination for banded matrices, or a conjugate gradient method for symmetric matrices and the ORTHOMIN method for asymmetric matrices.

II. Technical Information

II.1 Executables:

Operating System(s):

II.2 Source-code:

Programming Language(s): Programming language: ANSI standard FORTRAN 77 The source code is available upon request from the authors, please email:jsimunek@ussl.ars.usda.gov You will get 3.5 inch floppy containing source code and selected input and output files of several examples.

II.3 Manuals:

(see Source-code)

II.4 Data:

(see Source-code)

III. Mathematical Information

III.1 Mathematics

III.2 Quantities

III.2.1 Input

III.2.2 Output

IV. References

Simunek. J., Vogel T., van Genuchten M.Th., 1994. The SWMS_2D code for simulating water flow and solute transport in two-dimensional variably saturated media, Version 1.21. Research Report No. 132, 197 p., U.S. Salinity Laboratory, USDA, ARS, Riverside, California.
Simunek. J., van Genuchten M.Th., 1994. The CHAIN_2D code for simulating the two-dimensional movement of water, heat, and muliple solutes in variably saturated porous media, Version 1.1. Research Report No. 136, 194 p., U.S. Salinity Laboratory, USDA, ARS, Riverside, California.
van Genuchten, M.Th., Wagenet, R.J., 1989 Two-site/two-region models for pesticide transport and degradation: Theoretical development and analytical solutions, Soil Sci. Soc. Am.J., 53, 1303-1310.

V. Further information in the World-Wide-Web

VI. Additional remarks

The program is an extension of the SWMS_2D code for simulating water flow and solute transport in two-dimensional variably saturated media (Simunek et al. 1994). See also SWMS_3D
Last review of this document by: T. Gabele: 22. 6. 1997 -
Status of the document:
last modified by Tobias Gabele Wed Aug 21 21:44:40 CEST 2002

Go back to Register of Ecological Models (R E M)