transport in the unsaturated and saturated zones, we com- pared the model’s quasi 2-D predictions with those obtained
by a 2-D variably saturated flow and transport equations which were simulated by the 2DSOIL
10,18
and the SUTRA
22
numerical finite element models. The 2DSOIL code is partially based on the code SWMS_2D developed by
Simunek et al.
17
SUTRA is a code for simulation of fluid density dependent flow, and iterations procedure are exe-
cuted for both the flow and the transport equations at each time step. Since we do not consider problems of density
dependent flow and to reduce the computation time, the iterations for the transport equation in SUTRA were
‘frozen’. Three synthetic examples were considered.
4.1 Example 1. Spread of a groundwater ‘stripe’
The groundwater level at the initial time, t , is given as a
step function h
x ,
t ¼
h if
lxl R h
þ Dh
if lxl , R
22 where h
and the step Dh 3 R are prescribed. The analytical solution of the linearized 1-D Boussinesq equation for this
case, has the form
14
of h
x ,
t ¼
h þ
Dh 2
erf R ¹ x
2
at p
þ erf
R þ x 2
at
p 23
where a ¼ K
s
= S
y
˜h , S
y
is the specific yield and ˜h is the average groundwater level.
We carried out simulations for the silt loam GE 3 soil for which
21
v
s
¼ 0.369, v
r
¼ 0.131, K
s
¼ 0.0496 m per day, a ¼
0.423 m
¹ 1
and n ¼ 2.06. The longitudinal and transversal dispersivities were prescribed as a
L
¼ 1.0 m and a
T
¼ 0.1 m,
respectively. The simulated domain was presented by a rectangle of height 4 m from bottom of the aquifer to the
soil surface and 40 m length. The assigned initial condi- tions were h
¼ 2.0 m, Dh ¼ 0.5 m, and R ¼ 5.0 m. We note
the symmetry of eqn 22 at x ¼ 0. Hence, accordingly, the ]h
]x ¼ 0 condition was assigned. No flow condition was also specified at z ¼ 0 and z ¼ 4 m. At x ¼ 40 m, we
prescribed a constant head h ¼ 2 m. The initial solute con- centration was set to be C
¼ 1 for 0 x R and
h z h
þ Dh
, and C ¼
0 elsewhere. A finite difference grid of 17 3 17 nodes was used to solve the quasi 2-D
problem. The steps of the grid were 2.5 m and 0.25 m along x and z coordinate axes respectively. An equivalent
finite element grid the same number of nodes at the same locations was implemented for simulations with SUTRA
and 2DSOIL. The time step was increased by a factor of 1.1 starting from 10
¹ 6
day. Simulation with QUASI2D regard- ing groundwater level, was between the analytical solution
of the linearized Boussinesq equation and the numerical solution of the 2-D Richards equation, however, closer to
the latter one Fig. 2a. This is due to the fact that the quasi 2-D model accounts for both the specific features of the
variable saturation model and for the limitations of the Dupuit assumption. The maximum difference was 3 cm at
the groundwater summit x ¼ 0, where QUASI2D predicts higher groundwater level than the fully 2-D model, since the
first does not account for the horizontal water flux in the capillary fringe. The simulated distribution of the water
content in the unsaturated zone was in good agreement with the one obtained on the basis of the 2-D Richards
equation. The maximum difference between QUASI2D, 2DSOIL and SUTRA did not exceed 0.002 cm
3
cm
¹ 3
. The concentrations obtained by the quasi 2-D approach and
the fully 2-D flow and transport, compare well for x ¼ 0, 2.5 and 5.0 m Fig. 2b. For x ¼ 7.5 m there is a discre-
pancy between the three codes. However, absolute values of the concentration are relatively small there. Figure 2b
Fig. 2. Groundwater level a and concentration profiles b for the problem of ‘stripe spread’ example 1.
684 A. Yakirevich
et al.
demonstrates that SUTRA produces oscillatory solution in the last cross-section.
The computation time, for the period of 30 days, using QUASI2D, 2DSOIL and SUTRA is presented in Table 1.
We note that the QUASI2D code was several times faster than the 2DSOIL and SUTRA codes.
4.2 Example 2. Infiltration from the soil surface
