APPENDIX A
ADI FORMULATION OF COUPLED HEAT AND MASS TRANSFER MODEL
The partial differential equations governing the heat and mass
transfer in the soil were presented in Chapter 2 along with their
explicit finite difference expressions. Boundary conditions at the
soil surface and the lower boundary were also presented. An
alternating direction finite difference technique requires that
numerical expressions be formulated for the case of indexing the node
number from the soil surface to the lower boundary, then a second set
for use when the index is being changed in the other direction. The
equations for the forward direction (increasing node number) are
formulated by evaluating the spatial derivatives from the previous node
(j-1) to the current node (j) at the next time step (t+dt) which has
already been determined. Then the derivatives involving the node ahead
of the current node (j+1) is evaluated at the current time step. The
resulting equation is then solved for the value of the current node (j)
at the next time step (t+dt). The opposite is done when marching in
the backward direction (decreasing node number). The formulation for
the forward and backward marching difference equations is presented
below. The following are definitions of constants used in the
equations for either direction.
hhdZl WZ1
Bl = t Bl =
Fo
Ajdt
cs,jdwjdzj
DLjdt
dwjdzj"
Fv
Dvj(it
dwjdzj
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