4.5 Numerical example 5
Previous examples illustrate that our method is appropriately validated using the harmonic boundary conditions. Since the tidal variation is probably the major trigger inducing groundwater level fluctuation in coastal aquifers, the tidal fluctuation data are used to study tide–induced groundwater flow problem. This example is to evaluate the tidal and piezometer data at the Xing–Da port, Kaohsiung, Taiwan. The Xing–Da port is located in the Kaohsiung, southwestern Taiwan, as shown in Figure 14. The tidal data was from Yongan tidal station at 22°49’08.00” N latitude and 120°11’51.00” E longitude. The piezometer data was from Xing–Da groundwater observation well at 22°51’30.52” N latitude and 120°12’04.77” E longitude (Water Resources Agency, 2019).
The governing equation is described as Equation (1). The initial data is described as Equation (31). This study analyzed the tidal fluctuation data recorded at Xing–Da port from 00:00 pm on December 22 to 06:00 am on December 23, 2018, by the Ministry of Economic Affairs Water Resources Department, as shown in Figure 15. It is found that the highest hourly tidal fluctuation reached 0.85 m, whereas the lowest hourly tidal fluctuation may reach –0.29 m. Hence, the tidal boundary condition at left of the space domain is describes as
, (41)
where denotes the measured data by the Water Resources Agency, Ministry of Economic Affairs (2019), as shown in Figure 15. The boundary condition on the inland side is described as
. (42)
According to the Engineering Geological Investigation Data Bank by the Central Geology Survey of the Ministry of Economic Affairs (2019), the property of the confined aquifer and semi–permeable layer are sand and silt, respectively. The parameters used are listed in Table 3. The dimension of the length is 3000 (m). The transmissivity is 4.68 (m2/hr). The storage coefficient is . The leakage coefficient is (1/d). The final elapsed time is 30 (hr). The amplitude of the tidal change is 1 (m). The tidal period is 24 (hr).
There are 663 boundary points and one source point. The order of the basis function for the analysis is 15. To obtain the tide–induced groundwater fluctuation, we collocate 18631 inner points. Figure 16 demonstrates the comparison of measured data with the computed groundwater fluctuation using our method at m. Red line denotes the computed numerical results and gray square denotes the measured data. It is found that the computed results of the tide–induced groundwater head using the proposed method may agree with the measured data. Although there may be a shift in time in Figure 16, the overall behavior of the tide–induced groundwater head may be captured using our proposed method.