(1) Case A: Constant initial hydraulic head
The governing equation is described as Equation (1). In Case A, we consider the initial groundwater level to be constant. The initial data is
. (31)
The tidal boundary data at left of the space domain is described as
. (32)
The boundary data on the inland side is described as
. (33)
Equation (33) describes that the tide has nearly no effect if xapproaches far inland. The length is 3000 (m). The transmissivity is 31.25 (m2/hr). The storage coefficient is . The leakage coefficient is (1/d). The elapsed time is 65 (hr). The amplitude of the tidal change (A ) is 2.5 (m). The tidal period (t0) is 24.7 (hr).
Chen et al. (2013) applied the FDM to solve this problem. To apply the FDM, discretization in the spatial and temporal domains were separately considered. For spatial discretization, the governing equation of one–dimensional tide–induced groundwater response for each grid point was approximated using backward difference formulas. For time discretization, the implicit scheme was adopted (Chen et al., 2013). Since the proposed method is one of the meshfree approaches, this problem is solved by using the boundary collocation points placed on the spacetime boundary. Therefore, we adopt 163 boundary points uniformly distributed on the boundary and one source point. The Dirichlet data are provided on boundary points. The order of the basis function is 25. To yield the field solution, we collocate 2046 inner points. Numerical result of our method is then compared with that of the FDM. Figure 9 shows the numerical results adopting the FDM and our method. It is found that the tide–induced groundwater fluctuations computed using our method agreed well with those of the FDM.