Simulating discontinuous phenomena such as shock waves and wave breaking during wave propagation and run-up has been a challenging task for wave modeller. This requires a robust, accurate, and efficient numerical implementation. In this paper, we propose a two-dimensional numerical model for simulating wave propagation and run-up in shallow areas. We implemented numerically the 2-dimensional Shallow Water Equations (SWE) on a staggered grid by applying the momentum conserving approximation in the advection terms. The numerical model is named MCS-2d. For simulations of wet–dry phenomena and wave run-up, a method called thin layer is used, which is essentially a calculation of the momentum deactivated in dry areas, i.e., locations where the water thickness is less than the specified threshold value. Efficiency and robustness of the scheme are demonstrated by simulations of various benchmark shallow flow tests, including those with complex bathymetry and wave run-up. The accuracy of the scheme in the calculation of the moving shoreline was validated using the analytical solutions of Thacker 1981, N-wave by Carrier et al., 2003, and solitary wave in a sloping bay by Zelt 1986. Laboratory benchmarking was performed by simulation of a solitary wave run-up on a conical island, as well as a simulation of the Monai Valley case. Here, the embedded-influxing method is used to generate an appropriate wave influx for these simulations. Simulation results were compared favorably to the analytical and experimental data. Good agreement was reached with regard to wave signals and the calculation of moving shoreline. These observations suggest that the MCS method is appropriate for simulations of varying shallow water flow.

In this paper, we study the maximum run-up of solitary waves on a sloping beach and over a reef through a non-hydrostatic model. We do a modification on the non-hydrostatic model derived by Stelling and Zijlema. The model is approximated by resolving the vertical fluid depth into two-layer system. In contrast to the two-layer model proposed by Stelling, here, we have a block of a tridiagonal matrix for the hydrodynamic pressure. The equations are then solved by applying a staggered finite volume method with predictor-corrector step. For validation, several test cases are presented. The first test is simulating the propagation of solitary waves over a flat bottom. Good results in amplitude and shape preservation are obtained. Furthermore, run-up simulations are conducted for solitary waves climbing up a sloping beach, following the experimental set-up by Synolakis. In this case, two simulations are performed with solitary waves of small and large amplitude. Again, good agreements are obtained, especially for the prediction of run-up height. Moreover, we validate our numerical scheme for wave run-up simulation over a reef, and the result confirms the experimental data.

Evacuation of residents and diarrhea disease outbreak in evacuation zone have become serious problem that frequently happened during flood periods. Limited clean water supply and infrastructure in evacuation zone contribute to a critical spread of diarrhea. Transmission of diarrhea disease can be reduced by controlling clean water supply and treating diarrhea patients properly. These treatments require significant amount of budget, which may not be fulfilled in the fields. In his paper, transmission of diarrhea disease in evacuation zone using SIRS model is presented as control optimum problem with clean water supply and rate of treated patients as input controls. Existence and stability of equilibrium points and sensitivity analysis are investigated analytically for constant input controls. Optimum clean water supply and rate of treatment are found using optimum control technique. Optimal results for transmission of diarrhea and the corresponding controls during the period of observation are simulated numerically. The optimum result shows that transmission of diarrhea disease can be controlled with proper combination of water supply and rate of treatment within allowable budget.

This paper investigates the complex dynamics of thermal fluid flowwithin a porous rectangular cavity, subjected to a hybrid thermal environment consisting of differential heating on the top wall and uniform heat fluxes on the vertical boundaries. The study aims to characterize the interaction between buoyancy-driven convection and localized heat input within a saturated porous medium, modeled using the Darcy model. The governing equations are described by the continuity equation, the momentum equation, and the energy equation. The equations were made dimensionless. Three dimensionless parameters are introduced, namely the Darcy-Rayleigh number (the porous medium conductivity parameter), the heat flux parameter, and the geometric aspect ratio (the cavity shape parameter).Numerical solutionswere conducted by using the finite-difference method. Special attention is paid to finding an analytical solution for a small Darcy-Rayleigh number by using the asymptotic expansion method. Our simulation results show that the interaction between these boundary conditions creates complex, multi-cellular flow patterns and directly impacts heat transfer efficiency, offering insights for thermal management applications. Furthermore, the study provides a comprehensive mapping of the temperature distribution and streamline patterns, offering critical insights into heat transfer optimization.

Most water wave simulations use fixed boundaries. This simplification of course change the wave height prediction near the shore. In this paper, we will find a relation between reflected wave and incoming wave on a sloping beach. This result is important for later use in water wave simulations with moving boundaries. In this paper, we solve the 1-D nonlinear shallow water equation, using the conservative finite volume method. The scheme plus wet and dry procedure can simulate wave running up and down on a sloping beach. Comparison with Carrier and Greenspan analytical run up and down waves shows a good agreement. Then, we use this scheme to find a relation between reflected and incident wave on a sloping beach, incorporating the moving shoreline. And we obtain amplitude ratio and phase difference depending on wave frequency for moderate bottom slopes.