Coastal erosion is a major natural hazard along the northeastern shoreline (i.e., Yilan County) of Taiwan. Analyses of the evolution of the 0 m isobath of the Yilan County coastline indicate that erosion and accretion are occurring north and south of Wushi Fishery Port, respectively, because of jetty and groin construction. Topographic and bathymetric surveys involving the measurement of 43 cross sections were conducted in 2006, 2012, 2013, and 2019. The cross-shore profile comparisons reveal that the erosion of onshore dunes is significant in the northern Jhuan River estuary. Due to the establishment of a nature reserve in the southern Lanyang River estuary, the sediments are carried northward by tidal currents, and accretion is inevitable in the northern Lanyang River estuary. The results of the bathymetric surveys also suggest that the shoreline of Yilan County tends to accrete in summer because of abundant sediment from the rivers; however, it is eroded in winter, owing to the large waves induced by the northeast monsoon. Additionally, the calculated net volume of erosion and accretion between each pair of cross sections shows that the length of coastline impacted by estuarine sediment transport is approximately 2 km long from north to south along the coastline of the Lanyang River estuary.

Abstract:In this study, we used the natural and anthropogenic characteristics of a coastal region to generate risk maps showing vulnerability and potential hazards, and proposed design criteria for coastal defense and land use for the various kinds of risks faced. The Yunlin coast, a first-level protection area in mid-west Taiwan, was then used as an example to illustrate the proposed design criteria. The safety of the present coastal defenses and land use of the Yunlin coastal area was assessed, and coastal protection measures for hazard prevention were proposed based on the generated risk map. The results can be informative for future coastal management and the promotion of sustainable development of coastal zones.

In this article, we propose a novel meshless method for solving two-dimensional stationary heat conduction problems in layered materials. The proposed method is a recently developed boundary-type meshless method which combines the collocation scheme from the method of fundamental solutions (MFS) with the collocation Trefftz method (CTM) to improve the applicability of the method for solving boundary value problems. Particular non-singular basis functions from cylindrical harmonics are adopted in which the numerical approximation is based on the superposition principle using the non-singular basis functions expressed in terms of many source points. For the modeling of multi-layer composite materials, we adopted the domain decomposition method (DDM), which splits the domain into smaller subdomains. The continuity of the flux and the temperature has to be satisfied at the interface of subdomains for the problem. The validity of the proposed method is investigated for several test problems. Numerical applications were also carried out. Comparison of the proposed method with other meshless methods showed that it is highly accurate and computationally efficient for modeling heat conduction problems, especially in heterogeneous multi-layer composite materials.

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.

In this article, a novel spacetime collocation Trefftz method for solving the inverse heat conduction problem is presented. This pioneering work is based on the spacetime collocation Trefftz method; the method operates by collocating the boundary points in the spacetime coordinate system. In the spacetime domain, the initial and boundary conditions are both regarded as boundary conditions on the spacetime domain boundary. We may therefore rewrite an initial value problem (such as a heat conduction problem) as a boundary value problem. Hence, the spacetime collocation Trefftz method is adopted to solve the inverse heat conduction problem by approximating numerical solutions using Trefftz base functions satisfying the governing equation. The validity of the proposed method is established for a number of test problems. We compared the accuracy of the proposed method with that of the Trefftz method based on exponential basis functions. Results demonstrate that the proposed method obtains highly accurate numerical solutions and that the boundary data on the inaccessible boundary can be recovered even if the accessible data are specified at only one-fourth of the overall spacetime boundary.