Development of a Semi-analytical Dynamic Thrust Force Model

A moving water mass generates force which is exerted on its moving path. Cyclone generated storm surge or earthquake generated tsunami are specific examples of moving water mass the generates force along the coasts. In addition to human lives, these moving water masses cause severe damages to the coastal infrastructure due to tremendous force exerted on these structures. To assess the damage on these infrastructures, an essential parameter is the resultant force exerted on these structures. To evaluate the damages, there is hardly any quantitative method available to compute this force. In this paper we have developed a semi-analytical model, named as Dynamic Force Model (DFM), by using Variational Iteration Method to compute this force. As governing equations, we have used the Saint Venant equations which are basically 1D shallow water equations derived from the Navier-Stokes equations. The verified, calibrated and validated DFM is applied in Bangladesh coastal zone to compute dynamic thrust force due to tropical cyclone SIDR.

Numerical Simulation of Flood Routing using the Simplified Saint Venant Equations in Rectangular Channels

Floods, which cause a lot of damage, are a natural phenomenon that often occurs during the rainy season. Flood occurs because the discharge entering the channel exceeds the channel capacity. If the discharge data in the upstream area that will enter the channel is known, we can determine the flow behavior in the downstream area using a mathematical model. In this study, we proposed using simplified Saint Venant equations to simulate the flow routing in a prismatic channel with a rectangular section. This model is solved numerically using the finite difference method. Here, the numerical scheme used succeeds in simulating the flow behavior in the channel due to the discharge entering it. The simulation results show that the discharge entering the channel will propagate downstream with decreasing discharge quantity. Information on the amount of discharge at locations along the channel is useful as supporting data for flood control and prevention systems that will be conveyed to residents along the channel.Keywords: flood routing; prismatic channel; Saint Venant Equations; finite difference method. AbstrakBanjir yang menimbulkan banyak kerusakan merupakan fenomena alam yang sering terjadi pada musim hujan. Banjir terjadi karena debit yang masuk ke dalam kanal melebihi kapasitas kanalnya. Jika data debit di daerah hulu yang akan masuk ke dalam kanal diketahui, maka kita dapat menentukan perilaku aliran di daerah hilir dengan menggunakan model matematika. Dalam studi ini, kami mengusulkan untuk menggunakan persamaan Saint Venant yang disederhanakan untuk mensimulasikan penelusuran aliran pada saluran prismatik dengan penampang persegi panjang. Model ini diselesaikan secara numerik dengan menggunakan metode beda hingga. Di sini, skema numerik yang digunakan berhasil mensimulasikan perilaku aliran pada saluran akibat debit yang masuk. Hasil simulasi menunjukkan bahwa debit yang masuk ke saluran akan merambat ke hilir dengan kuantitas debit yang semakin berkurang. Informasi jumlah debit di lokasi sepanjang saluran ini berguna sebagai data pendukung pada sistem pengendalian dan pencegahan banjir yang akan disampaikan kepada penduduk di sepanjang kanal.Kata kunci: penelusuran banjir; saluran prismatik; persamaan Saint Venant; metode beda hingga.

The Momentum Conserving Scheme Implementation for Simulating Dambreak Flow in a Channel with Various Contractions

Rapid flow downstream due to dambreak has a detrimental effect on the surrounding environment or, more dangerously, can be life-threatening. From a practical point of view, these flows are important to studies due to the limited dambreak real case data. This paper discusses the numerical modelling of the dambreak flow through a channel with three different contractions. Our goal here is to investigate the performance of a numerical model for solving the Saint-Venant equations using a momentum conserving staggered grid scheme (MCS). The scheme is the conservative formulation of the governing equations. Flows across channels of various widths and depths have been successfully simulated using a version of this scheme. In this work, we extend our previous work by simulating dambreak flow in a wave tank through several forms of contraction; trapezoidal and triangular. Our simulation results show good agreement with the experimental data in the literature. This assessment shows the merit of the scheme, which is suitable for dambreak flows in channels of varying width.

The Waterlogging Process Model in the Paddy Fields of Flat Irrigation Districts

Flat, low-lying agricultural areas such as irrigation districts in southern China have been increasingly vulnerable to flood inundation disasters because of the increased runoff associated with urbanization and climate change. In this study, we developed a waterlogging process simulation model comprising two parts: runoff generation module and runoff confluence module. An improved tank model and hydrodynamic model based on Saint–Venant equations were adopted in the runoff generation and confluence module, respectively. The results show that the model’s relative error and root mean square error are 2.1% and 0.17 mm/h, and the Nash coefficient of the model is 0.91. The relative error of river level simulation was within 5%, and the Nash coefficient was higher than 0.9. The proposed waterlogging simulation model could be a valuable tool for describing the process of waterlogging generation, accumulation, and confluence in the studied irrigation district or other regions with similar climatic conditions.

Comparison between two generalized Nash models with a same non-zero initial condition

Initial condition can impact the forecast precision especially in a real-time forecasting stage. The discrete linear cascade model (DLCM) and the generalized Nash model (GNM), though expressed in different ways, are both the generalization of the Nash cascade model considering the initial condition. This paper investigates the relationship and difference between DLCM and GNM both mathematically and experimentally. Mathematically, the main difference lies in the way to estimate the initial storage state. In the DLCM, the initial state is estimated and not unique, while that in the GNM is observed and unique. Hence, the GNM is the exact solution of the Nash cascade model, while the DLCM is an approximate solution and it can be transformed to the GNM when the initial storage state is calculated by the approach suggested in the GNM. As a discrete solution, the DLCM can be directly applied to the practical discrete streamflow data system. However, the numerical calculation approach such as the finite difference method is often used to make the GNM practically applicable. At last, a test example obtained by the solution of the Saint-Venant equations is used to illustrate this difference. The results show that the GNM provides a unique solution while the DLCM has multiple solutions, whose forecast precision depends upon the estimate accuracy of the current state.

Analytic Normalized Solutions of 2D Fractional Saint-Venant Equations of a Complex Variable

Saint-Venant equations describe the flow below a pressure surface in a fluid. We aim to generalize this class of equations using fractional calculus of a complex variable. We deal with a fractional integral operator type Prabhakar operator in the open unit disk. We formulate the extended operator in a linear convolution operator with a normalized function to study some important geometric behaviors. A class of integral inequalities is investigated involving special functions. The upper bound of the suggested operator is computed by using the Fox-Wright function, for a class of convex functions and univalent functions. Moreover, as an application, we determine the upper bound of the generalized fractional 2-dimensional Saint-Venant equations (2D-SVE) of diffusive wave including the difference of bed slope.

Development of an algorithm for calculating stable solutions of the Saint-Venant equation using an upwind implicit difference scheme

The problem of numerical determination of Lyapunov-stable (exponential stability) solutions of the Saint-Venant equations system has remained open until now. The authors of this paper previously proposed an implicit upwind difference splitting scheme, but its practical applicability was not indicated there. In this paper, the problem is solved successfully, namely, an algorithm for calculating Lyapunov-stable solutions of the Saint-Venant equations system is developed and implemented using an upwind implicit difference splitting scheme on the example of the Big Almaty Canal (hereinafter BAC). As a result of the proposed algorithm application, it was established that: 1) we were able to perform a computational calculation of the numerical determination problem of the water level and velocity on a part of the BAC (10,000 meters) located in the Almaty region; 2) the numerical values of the water level height and horizontal velocity are consistent with the actual measurements of the parameters of the water flow in the BAC; 3) the proposed computational algorithm is stable; 4) the numerical stationary solution of the system of Saint-Venant equations on the example of the BAC is Lyapunov-stable (exponentially stable); 5) the obtained results (according to the BAC) show the efficiency of the developed algorithm based on an implicit upwind difference scheme according to the calculated time. Since we managed to increase the values of the difference grid time step up to 0.8 for calculating the numerical solution according to the proposed implicit scheme.

Viability of OpenFOAM as the Numerical Engine for Augmented Reality Sandbox

Many augmented reality sandboxes use a single purpose implementation of standard numerical schemes to solve the Saint-Venant equations for shallow water in real time. This work evaluates the open-source computational fluid dynamics (CFD) package OpenFOAM as an alternative to the custom implementations traditionally used. Many sandboxes are used in educational and research settings and CFD engines with costly licensing was not desirable. The goal of this work is to identify or create an OpenFOAM solver that handles features such as dry conditions and complex topographies. The existing shallowWaterFoam solver was identified as the best candidate but required modification to handle scenarios representative of the target application. Replacing the existing custom numerical algorithm with the OpenFOAM software will more easily allow future incorporation additional phenomena.

Application of Smooth Particle Hydrodynamics to Particular Flow Cases Solved by Saint-Venant Equations

Smoothed particle hydrodynamics (SPH) is a Lagrangian mesh free particle method which has been developed and widely applied to different areas in engineering. Recently, the SPH method has also been used to solve the shallow water equations, resulting in (SPH-SWEs) formulations. With the significant developments made, SPH-SWEs provide an accurate computational tool for solving problems of wave propagation, flood inundation, and wet-dry interfaces. Capabilities of the SPH method to solve Saint-Venant equations have been tested using a SPH-SWE code to simulate different hydraulic test cases. Results were compared to other established and commercial hydraulic modelling packages that use Eulerian approaches. The test cases cover non-uniform steady state profiles, wave propagation, and flood inundation cases. The SPH-SWEs simulations provided results that compared well with other established and commercial hydraulic modeling packages. Nevertheless, SPH-SWEs simulations experienced some drawbacks such as loss of inflow water volume of up to 2%, for 2D flood propagation. Simulations were carried out using an open source solver, named SWE-SPHysics.