53
that of the standard explicit methods. Increased stability is obtained
over the standard explicit methods but is less than that for the
implicit techniques. This implies that using the same grid spacing, a
larger time step can be used in the ADI methods than that for explicit
methods.
An ADI finite difference technique was used to solve the system of
equations for the soil profile due to the increased stability
characteristics over explicit methods. Appendix A contains a detailed
development of the numerical equations used in the ADI technique.
Hydraulic (equation 2-40) and thermal properties (equations 2-35 and
2-36) of the soil and the surface transfer coefficients (equations 2-50
and 2-51) were calculated at the beginning of each time step. A
general description of the solution algorithm is shown in Figure (2-6).
The energy and water equations were solved for the temperature and
volumetric water content, respectively at the next time step. The
equilibrium condition was used to determine the vapor concentration by
substitution of the values of soil temperature, water content, water
potential, and saturated vapor concentration in equation (2-30). The
vapor continuity equation was used to determine the evaporation rate.
The calculations were repeated using the new evaporation rate
until the absolute value of the maximum fractional change in any of the
variables was less than a prescribed convergence criterion.
The system of numerical equations was solved using computer code
written in FORTRAN77. A variable grid spacing was used throughout the
soil profile with the smaller mesh being located near the soil surface
due to expected large gradients in temperature and moisture content
once the soil surface begins to dry (Table 2-3). The program was then