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.

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 study, we developed a novel boundary-type meshless approach for dealing with two-dimensional transient flows in heterogeneous layered porous media. The novelty of the proposed method is that we derived the Trefftz space–time basis function for the two-dimensional diffusion equation in layered porous media in the space–time domain. The continuity conditions at the interface of the subdomains were satisfied in terms of the domain decomposition method. Numerical solutions were approximated based on the superposition principle utilizing the space–time basis functions of the governing equation. Using the space–time collocation scheme, the numerical solutions of the problem were solved with boundary and initial data assigned on the space–time boundaries, which combined spatial and temporal discretizations in the space–time manifold. Accordingly, the transient flows through the heterogeneous layered porous media in the space–time domain could be solved without using a time-marching scheme. Numerical examples and a convergence analysis were carried out to validate the accuracy and the stability of the method. The results illustrate that an excellent agreement with the analytical solution was obtained. Additionally, the proposed method was relatively simple because we only needed to deal with the boundary data, even for the problems in the heterogeneous layered porous media. Finally, when compared with the conventional time-marching scheme, highly accurate solutions were obtained and the error accumulation from the time-marching scheme was avoided.

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.

In this article, a newly developed multiple-source meshless method (MSMM) capable of solving inverse heat conduction problems in two dimensions is presented. Evolved from the collocation Trefftz method (CTM), the MSMM approximates the solution by using many source points through the addition theorem such that the ill-posedness is greatly reduced. The MSMM has the same superiorities as the CTM, such as the boundary discretization only, and is advantageous for solving inverse problems. Several numerical examples are conducted to validate the accuracy of solving inverse heat conduction problems using boundary conditions with different levels of noise. Moreover, the domain decomposition method is adopted for problems in the doubly-connected domain. The results demonstrate that the proposed method may recover the unknown data with remarkably high accuracy, even though the over-specified boundary data are assigned a portion that is less than 1/10 of the overall domain boundary.

A coastal erosion risk assessment was framed as the basis for the intervention of coastal adaptation strategies under time-variant scenarios. The framework was devised to assess the influence of coastal erosion on coastal defense, the coastal inundation induced by the erosion-induced malfunction of defense, and risks using a downscaling analysis and the mechanism of the compound hazard interaction, which are innovative and practical for the application of coastal management in Taiwan. In addition, the vulnerable socio-economy was also taken into consideration in risk assessment. The adaptive strategy is proposed in terms of the risk origins and time-variance of risk forecasts, and the risk origins were assessed based on the Fuzzy Delphi Method and the analytic hierarchy process instead of subjective consideration. Within the erosion-induced hazard and risk assessments, this study considered erosion rates, decreases in defense elevation due to land subsidence, and population development in time-variant scenario analyses to estimate risk forecasts. Furthermore, a case study of the Yunlin coastal area was undertaken to demonstrate the feasibility of the proposed method. The presented results are informative for coastal hazard reduction and the promotion of the sustainable development of coastal zones.