Modeling Tide–induced Groundwater Response in a Coastal Confined Aquifer Using the Spacetime Collocation Approach

Abstract

This paper presents the modeling of tide-induced groundwater response using the spacetime collocation approach (SCA). The newly developed SCA begins with the consideration of Trefftz basis functions which are general solutions of the governing equation deriving from the separation of variables. The solution of the groundwater response in a coastal confined aquifer with an estuary boundary where the phase and amplitude of tide can vary with time and position is then approximated by the linear combination of Trefftz basis functions using the superposition theorem. The SCA is validated for several numerical examples with analytical solutions. The comparison of the results and accuracy for the SCA with the time-marching finite difference method is carried out. In addition, the SCA is adopted to examine the tidal and groundwater piezometer data at the Xing-Da port, Kaohsiung, Taiwan. The results demonstrate the SCA may obtain highly accurate results. Moreover, it shows the advantages of the SCA such that we only discretize by a set of points on the spacetime boundary without tedious mesh generation and thus significantly enhance the applicability.

Modeling Transient Flows in Heterogeneous Layered Porous Media Using the Space–Time Trefftz Method

“…The space-time Trefftz method utilizing Trefftz functions originates from the Trefftz method [12,21,24]. For a simply connected domain, one usually locates the source point in the space-time domain; the number of source points is only one for the proposed space-time Trefftz method.…”

“…A variety of mesh-generated techniques, such as the boundary element method [13], finite element method [14,15], finite volume method [16,17], and finite difference method [18,19], have been proposed to analyze heterogeneous layered porous media. In contrast with conventional mesh-generated techniques, meshfree approaches have attracted much attention in recent years because of their characteristics of simplicity, meshfree, and the capability to deal with engineering problems with complex geometry [20][21][22][23][24][25][26]. Of the wide variety of meshfree approaches, the Trefftz method is one of the widespread boundary-type meshless methods for dealing with steady-state Laplace-type problems, where computed results are approximated as a series of basis functions, completely satisfying the governing Laplace-type equations [27][28][29].…”