(2) Case B: Inclined initial hydraulic head
In Case B, the head of the sea side is a function of distance x .
The governing equation is described as Equation (1). The initial data is
. (34)
The boundary conditions at both left and right sides are expressed as
, (35)
. (36)
In this example, , and . Other parameters including the dimension of the
space domain, the transmissivity, the storage coefficient, the leakage
coefficient, the elapsed time, the amplitude of the tidal change, and
the tidal period are the same as Case A.
This example is solved using both FDM and our method. For the FDM
analysis, the temporal and spatial discretizations for this problem are
separately considered. The implicit scheme and the central difference
approximation are considered for the temporal and spatial
discretization, respectively. For the SCA analysis, we consider 163
boundary points and one source point. The order of the basis function
for the analysis is 25. Figure 10 depicts the results computed utilizing
the FDM and our method. It is found that the tide–induced groundwater
response computed using the proposed method agreed well with those of
the FDM.