Quoted from: https://www.ars.usda.gov/pacific-west-area/riverside-ca/agricultural-water-efficiency-and-salinity-research-unit/docs/model/chain-2d-model/ 

CHAIN-2D is a computer program 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 heat and solute 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 equations also include provisions for nonlinear nonequilibrium reactions between the solid and 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 vertical 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 the conjugate gradient method for symmetric matrices, or the ORTHOMIN method for asymmetric matrices. The program is written in ANSI standard FORTRAN 77. Computer memory is a function of the problem definition. This report serves as both a user manual and reference document. Detailed instructions are given for data input preparation. Example input and selected output files are also provided.

References

Simunek, J. and M. Th. van Genuchten. 1994. The CHAIN_2D Code for Simulating Two-Dimensional Movement of Water, Heat, and Multiple Solutes in Variably-Saturated Porous Media, Version 1.1. Research Report No. 136,
U. S. Salinity Laboratory, USDA, ARS, Riverside, California.