Although many numerical techniques such as approximate Riemann solvers can be used to analyze subcritical and supercritical flows modeled by hyperbolic-type shallow-water equations, there are some difficulties in practical applications due to the numerical unbalance between source and flux terms. In this study, a revised surface gradient method is proposed that balances source and flux terms. The new numerical model employs the MUSCL–Hancock scheme and the HLLC approximate Riemann solver. Several verifications are conducted, including analyses of transcritical steady-state flows, unsteady dam break flows on a wet and dry bed, and flows over an irregular bathymetry. The model consistently returns accurate and reasonable results comparable to those obtained through analytical methods and laboratory experiments. The revised surface gradient method may be a simple but robust numerical scheme appropriate for solving hyperbolic-type shallow-water equations over an irregular bathymetry.

A combination of a deterministic approach and fragility analysis is applied to assess tsunami damage caused to buildings. The area selected to validate the model is Imwon Port in Korea. The deterministic approach includes numerical modeling of tsunami propagation in the East Sea following an earthquake on the western coast of Japan. The model is based on the linear shallow-water equations (LSWE) augmented with Boussinesq approximation to account for dispersion effects in wave propagation, and coastal wave run-up is modeled by non-linear shallow-water equations (NLSWE). The output from the deterministic model comprises inundation depth. The numerical output is used to perform fragility analysis for buildings vulnerable to flooding by tsunamis in the port area. Recently developed fragility curves—based on the ordinal regression method—are used for damage probability estimates. The extent of structural damage in the areas under a tsunami hazard is identified by the numerical modeling of tsunami features. Our numerical model offers high bathymetric resolution, which enables us to capture flow features at the individual structure level and results in improved estimation of damage probability. This approach can serve as a measure of assessing structure vulnerability for areas with little or no records of tsunami damage and provide planners with a better understanding of structure behavior when a tsunami strikes.

Accurate flood risk assessment is useful for mitigating the hazards of dam break floods. Flood inundation may cause serious damage to human lives, property, and river environments. In many countries, flood risks are assessed to establish flood mitigation plans against unexpected flood events. Flood risk maps are based on inundation depth and maximum flow velocity obtained from numerical models based on shallow-water equations. Flood intensity, defined as the product of flood depth and velocity, is used to assess risk in vulnerable areas of many European countries. The inundation flow is affected by structures such as buildings and houses. In this study, changes in water depth, velocity, and flood intensity that are associated with arrangements of structures are numerically investigated. A numerical model is formulated using a finite volume approach and is first verified for available test problems. The effects of structures are then tested by measuring flood characteristics in an experimental basin in which various arrangements of model structures are placed. The measured flood characteristics are then compared to the numerical results.

Tsunamis are distinguished from ordinary waves and currents owing to their characteristic longer wavelengths. Although the occurrence frequency of tsunamis is low, it can contribute to the loss of a large number of human lives as well as property damage. To date, tsunami research has concentrated on developing numerical models to predict tsunami heights and run-up heights with improved accuracy because hydraulic experiments are associated with high costs for laboratory installation and maintenance. Recently, artificial intelligence has been developed and has revealed outstanding performance in science and engineering fields. In this study, we estimated the maximum tsunami heights for virtual tsunamis. Tsunami numerical simulation was performed to obtain tsunami height profiles for historical tsunamis and virtual tsunamis. Subsequently, Bayesian neural networks were employed to predict maximum tsunami heights for virtual tsunamis.