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A spillway is a hydraulic structure of major importance in dam safety, and its current analysis usually involves a hybrid approach combining CFD modeling with experimental research, either using well-known WES design charts or conducting new model experiments in the laboratory. Flow over spillway crests involves fluid accelerations, making irrotationality an adequate simplification of the Navier–Stokes (NS) equations. However, an efficient tool using this method is currently lacking for spillway flow, particularly for ogee spillway flow. This work focuses on this aspect of the problem, and a new method for computing irrotational flow solutions over ogee spillways is proposed by developing flow net computational solutions. The proposed method entails a new iterative procedure in the complex potential plane where free surface pressures are exactly set to zero, contrary to other methods, and an automatic determination of the critical point, the unknown energy head, and the free surface profile. The model generates solutions efficiently in only a few seconds on a personal workstation, permitting a fast estimate of spillway flow operation, and is thus an effective complement to experimental and NS-CFD modeling. The solutions produced are compared with observations of a high operational head equal to five times the design head of the ogee crest, resulting in reasonable agreement. The application of the new model to investigate the limitations of analytical equations used in spillway flow, like Jaeger's theory, establishes limits for its use by relating its curvature parameter to the spillway chute slope. [ABSTRACT FROM AUTHOR]

Performance of a new incompressible smoothed particle hydrodynamics (I-SPH) model for simulating free surface flows using Lagrangian description of motion is numerically evaluated. In the SPH method, kernel or weight functions are used for approximation of a function and its spatial derivatives based on the theory of integral interpolants exhibiting poor accuracy. In this study, the pressure field is obtained by solving a pressure Poisson equation that is derived from a two-step prediction–correction approach applied for temporal discretization of the governing equations of fluid flows and enforcement of incompressibility. A newly developed gradient model in the context of the mesh-less moving particle semi-implicit (MPS) method is applied to improve the standard gradient and Laplacian models of I-SPH method in the proposed approach. The higher accuracy of the modified SPH scheme, which is a kernel gradient-free model, in comparison with the standard I-SPH method is validated trough solving the classic benchmark problems including the dam break flow, solitary wave propagation, standing wave motion, liquid sloshing and water drop stretching. [ABSTRACT FROM AUTHOR]

Numerical methods are very useful for predicting water levels, velocities and flow rates in hydraulic systems. The Saint-Venant system of equations, which is a hyperbolic partial differential system, is widely used in the modelling of a flood wave due to a dam failure. In this study, two explicit finite difference Lax-Friedrichs and modified Lax-Friedrichs numerical schemes are used to simulate the failure wave of a dam. The calibration of the obtained results is done in relation to experimental measurements and numerical results existing in the literature specialized in this field of research. The experimental set-up consists of a water reservoir that simulates the reservoir of a dam, followed downstream by a horizontal dry bottom section, a triangular bottom sill with steep slopes and a small tide of water at rest after the triangular obstacle which ends with a vertical diaphragm. The simulation obtained results with the new formulation of the Lax-Friedrichs numerical scheme showed good agreement with the simulated, experimental and numerical results of other researchers. [ABSTRACT FROM AUTHOR]

A new reformulation of a free boundary problem for the Stokes equations, which govern a viscous flow with an overdetermined condition on the free boundary, is proposed. The idea of the method is to transform the governing equations into a boundary value problem with a complex Robin boundary condition that couples the two boundary conditions on the free boundary. The proposed formulation gives rise to a new cost functional that apparently has not been exploited in the context of free surface problems. The shape derivative of the cost function, constructed using the imaginary part of the velocity and pressure solution in the whole domain, is computed in order to identify the free boundary. The shape gradient information is then utilized in a domain variation method based on a preconditioned steepest descent algorithm to solve the shape optimization problem. Numerical results illustrating the applicability of the method are provided in both two and three spatial dimensions. For validation and evaluation of the method, the numerical results are compared with those obtained via the classical tracking-Dirichlet-data cost functional approach. [ABSTRACT FROM AUTHOR]

A spillway is a hydraulic structure of major importance in dam safety, and its current analysis usually involves a hybrid approach combining CFD modeling with experimental research, either using well-known WES design charts or conducting new model experiments in the laboratory. Flow over spillway crests involves fluid accelerations, making irrotationality an adequate simplification of the Navier–Stokes (NS) equations. However, an efficient tool using this method is currently lacking for spillway flow, particularly for ogee spillway flow. This work focuses on this aspect of the problem, and a new method for computing irrotational flow solutions over ogee spillways is proposed by developing flow net computational solutions. The proposed method entails a new iterative procedure in the complex potential plane where free surface pressures are exactly set to zero, contrary to other methods, and an automatic determination of the critical point, the unknown energy head, and the free surface profile. The model generates solutions efficiently in only a few seconds on a personal workstation, permitting a fast estimate of spillway flow operation, and is thus an effective complement to experimental and NS-CFD modeling. The solutions produced are compared with observations of a high operational head equal to five times the design head of the ogee crest, resulting in reasonable agreement. The application of the new model to investigate the limitations of analytical equations used in spillway flow, like Jaeger’s theory, establishes limits for its use by relating its curvature parameter to the spillway chute slope.

The present research used a combination of experimental and numerical methods to investigate energy dissipation blocks of different heights placed downstream of a sluice gate in an open channel flow. Numerical model simulations were performed using a 3D computational fluid dynamics (CFD) technique, using the Reynolds-averaged Navier-Stokes (RANS) equations with the volume of fluid (VOF) and k-ε turbulence models. The accuracy of the numerical model and the grid sensitivity was assessed according to a recommended procedure in the literature. Different hydraulic and geometry conditions were investigated to understand the energy dissipation behaviour of the blocks. The hydrodynamic effects of different block spacings, heights and configurations were analysed by means of CFD simulations. The results show that the variable size blocks have a high energy dissipation efficiency in sluice gate flows, particularly at high Froude numbers. The energy dissipation efficiency of the blocks downstream of a sluice gate can reach up to 55% for high discharges (Q = 35 L/s). Interestingly, the energy dissipation performance of small gate openings exceeds that of large gate openings, reaching a peak efficiency of 40% for the same discharge. In addition, the block spacing has a minimal effect on the energy dissipation, while smaller block spacing results in a smoother water surface profile. [ABSTRACT FROM AUTHOR]

This paper describes a 2D‐3D hybrid model for tsunami simulations that uses an overlapping method based on an arbitrary grid. A 2D model is used to simulate wave propagation from the source area to the offshore area, and a 3D model is then used to simulate the free surface flow around structures in coastal areas. An overlapping method that satisfies the conservation and compatibility conditions is developed to couple the two models. The shallow water equations are applied for the 2D model, and the Navier‐Stokes equations and continuity equations are applied for the flow field of the 3D model. The Allen‐Cahn equation is applied for the interface‐capturing method of the 3D model. The stabilized finite element method is applied for the spatial discretization and the Crank‐Nicolson method is used for the temporal discretization of the governing equations. The model is verified and validated through several numerical analysis examples. [ABSTRACT FROM AUTHOR]

Hydraulic engineering applications require a good knowledge of turbulent behaviour in non-prismatic channels. This paper aims to predict turbulent behaviour using large-eddy simulation (LES). The model channel has a warped transition. We perform two-phase LES of free-surface flow and validate the results using experimental data and benchmark solution. We discuss rigorous strategies for model set-up, parameter selection and parametric value assignment, including parameters in spectrum synthesiser (SS) and vortex method (VM) for inlet turbulence. The predicted flow displays complex structures due to eddy motions translated from upstream and locally generated by asymmetrical separation in the transition. The history of the flow dynamics may affect the flow development. The predicted velocity, energy spectrum, root-mean-square error, hit-rate and factor-of-two compare well with measurements and benchmark solution. Mapping mean-velocity distribution from experimental data, combined with SS, gives satisfactory inlet condition; alternatively, a 1/7th power-law for the mean-velocity, combined with VM, is acceptable. This paper uses the Okubo–Weiss parameter to delineate instantaneous coherent structures. The LES methods are reliable, efficient and cost-effective. As compared to the simulation of prismatic channels, the flow dynamics in non-prismatic channels exhibit flow separation and turbulence interactions, which increase the flow-complexity, while offering results with crucial practical applications. HIGHLIGHTS Key features of turbulence are revealed by two-phase LES of free surface flow in expansion.; Effective and practical methods for open-boundary treatments, flow initialisations and turbulence closures are explored.; Instantaneous eddy structures are delineated using the Okubo–Weiss parameter.; An upstream channel section eight times the flow depth is recommended for LES of flow in expansion.;

The dam break flow poses a common free surface flow problem in hydraulic engineering, and its ac- curate simulation is of great engineering significance. The B-spline material point method (BSMPM), as an im- proved algorithm of the material point method (MPM), has optimized accuracy and convergence in material point calculations and unique algorithmic advantages in free surface flow problems. Based on the BSMPM, a weakly compressible BSMPM (WC-BSMPM) was developed through introduction of an artificial equation of state. The simulation of the dam break flow problem was carried out, with the effects of the order of the B- spline interpolation basis function on the simulation results analyzed. The results show that, the simulated fluid wave front position, the wavefront velocity and the elevation variation at a given position are basically consistent with the existing experimental results. As the order of the basis function increases, the computation time will lengthen for about 1.5 times. However, the computation times of the BSMPM of different orders will uniformly increase approximately linearly with the background grid size. The validity of the WC-BSMPM simulation of the dam break flow problem was verified. The research provides a new idea and method for the simulation of dam break flow problems. [ABSTRACT FROM AUTHOR]

Hydrodynamic noise from an air-water interface is often encountered in marine engineering structures. It involves a complex mechanism, various forms of sound sources and many factors affecting the propagation. It interacts with the free surface and is affected by cavitation and water-air-bubble mixed flow, which has a negative impact on the concealment of the ship, giving this line of inquiry strong research significance. This paper introduces a noise calculation method and its applications in terms of free surface noise, cavitation noise and water-air-bubble mixed flow noise respectively, and describes their computational methods and key issues. The solutions currently in use are also introduced. Finally, future research directions are proposed.

It is known that free-surface flows with small slopes can be described by classical lubrication theory. By replacing the assumption of quasi-parallel flows with local wedge flows, the classical lubrication theory has been generalized to the situation with finite surface slopes and vanishing fluxes, e.g., steady capillary flows with moving contact lines. In this work, this theory is further extended by imposing the contribution of finite fluxes, which can be modeled by a source/sink flow in a wedge. The resulting lubrication equation is used to investigate the surface morphologies observed in dip coating of an inclined plate, including the Landau-Levich-Derjaguin film, dimple and capillary shock. Dependence of these structures on the inclination angle and relative speed with respect to the plate is discussed in detail. Numerical solutions of the lubrication equation agree well with available asymptotic theory. [ABSTRACT FROM AUTHOR]

In this research, a numerical investigation was carried out on the effect of obstacle presence on the water flow during the dam-break in a dry bed. The validity of the numerical simulations was confirmed after comparing the results with the experimental evidence. Rectangular, trapezoidal and triangle obstacles were simulated numerically to explain the obstacle effect on the water flow. Water surface tracking and turbulent flow were modeled using the Volume of Fluid (VOF) method and the standard k-ω model, respectively. Pressure and velocity variations during the dam-break flow are presented and analyzed. HIGHLIGHTS Simulation of dam-break flow.; Presence of an obstacle in the flow.; Different obstacle geometries.; Numerical verification of water surface.; Pressure distributions during flow after dam-break.;

The violent fluid motion in a partially filled vessel is called sloshing. Resonance occurs when the natural frequency of the fluid oscillation approaches that of its container. This result may lead to structural failure. In this study, a Smoothed Particle Hydrodynamics (SPH) model is established to investigate the sloshing motion in a shallow water reservoir. Sloshing in a submerged obstacle, cylinder array, rectangular and wall-inclined topography is considered. In terms of results, the cylinder array is more effective than the other models to reduce the impact force due to the sloshing wave in a rectangular tank. The results prove that the proposed SPH model is capable of simulating sloshing in the shallow water tank.

The accurate and efficient simulation for violent free surface flow with intense splashing is import in engineering. The purpose of this paper was to extend and validate the capabilities of Sunway Lattice Boltzmann Method code (SWLBM, our in-house developed CFD framework) in simulating large-scale three-dimensional violent free surface flow. The lattice Boltzmann method was employed to solve the fluid dynamics. The interface was captured by the single-phase free surface model. For parallel computing, the computational domain was divided into parallel blocks and overlap layers were designed for inter-block communications. Several typical dam-break problems were selected for validating the ability of reproducing splashing details, where finest spatial resolution was up to about 0.6 billion cells. The numerical results were in good agreement with experimental results. The present results revealed more plentiful splashing details than various published results with relatively coarser spatial resolution. The efficiency of SWLBM was over 100 times higher than that of OpenFOAM in the testing example. It was demonstrated that SWLBM is capable of simulating large-scale violent free surface flow and reproducing splashing details with sufficient accuracy and efficiency. SWLBM has the potential to be applied in real engineering problems including simulating wave impact on decks. • The capabilities of free surface simulation have been extended for the LBM-based framework SWLBM. • The accuracy and robustness of SWLBM were validated through various dam-break cases. • Large-scale simulations for free surface flow with up to 0.6 billion lattice cells were achieved. • Much more plentiful splashing details are reproduced compared with existing relevant literature. • The efficiency of SWLBM was over 100 times higher than that of OpenFOAM in the testing example. [ABSTRACT FROM AUTHOR]

In this work we present a robust finite element procedure for modeling 3D nonlinear liquid sloshing phenomena using standard potential theory. A well known issue in simulating inviscid free-surface flows is an onset of spurious oscillations ("saw-tooth") caused by numerical instabilities. Here we demonstrate that a novel post-processing procedure, based on the Savitzky–Golay filtering algorithm allows us to overcome this challenge. It is shown that unphysical numerical oscillations are smoothed out and nodal free-surface position along with velocity values are accurately recovered from conventional finite element analysis. Sloshing dynamics (limited to non-overlapping waves) is investigated for a partially filled vertical circular cylinder subjected to a broad range of harmonic and ElCentro seismic excitations. The results compare well with those obtained with finite volume OpenFOAM software. One-way coupling FSI analysis is also included to estimate stress and deflection experienced by cylindrical containers. • Robust FE solution of 3D nonlinear sloshing dynamics modeled by potential theory. • Savitzky-Golay filtering for effective and accurate numerical oscillation smoothing. • One-way FSI analysis which includes stress and deflection parametric study. • Sloshing induced by seismic excitation for small to steep non-overlapping waves. [ABSTRACT FROM AUTHOR]

A finite element model utilizing the σ-transform is presented to address the two-dimensional fully nonlinear potential flow problem. The Euler–Zakharov equation, discretized with Hermite elements, serves as the time-dependent free surface boundary condition. Higher-order accuracy is achieved through polynomial approximations in the vertical dimension. Temporal discretization employs the explicit Runge-Kutta method with adaptive step size. Convergence studies and stability assessments for long-time simulations are conducted. Model accuracy is validated through two cases of wave propagation over a trapezoidal bar. The results demonstrate high efficiency and rapid convergence under finite water depth conditions. Comparison with experimental data confirms the method's accuracy in predicting the propagation and dispersion of nonlinear water waves. • A two-dimensional σ-transform based finite element method has been presented for simulating fully nonlinear potential flow. • Most numerical integrations are calculated once for all in advance, which greatly speeds up the computation. • The convergence, stability, and accuracy of the method are verified by analytical and experimental data. • This method can accurately simulate the propagation and dispersion of strong nonlinear waves in finite water depth. [ABSTRACT FROM AUTHOR]

This paper proposes the notion of model adaptivity for fluid flow modelling, where the underlying model (the governing equations) is adaptively changed in space and time. Specifically, this work introduces a hybrid and adaptive coupling of a 3D bulk fluid flow model with a 2D thin film flow model. As a result, this work extends the applicability of existing thin film flow models to complex scenarios where, for example, bulk flow develops into thin films after striking a surface. At each location in space and time, the proposed framework automatically decides whether a 3D model or a 2D model must be applied. Using a meshless approach for both 3D and 2D models, at each particle, the decision to apply a 2D or 3D model is based on the user-prescribed resolution and a local principal component analysis. When a particle needs to be changed from a 3D model to 2D, or vice versa, the discretization is changed, and all relevant data mapping is done on-the-fly. Appropriate two-way coupling conditions and mass conservation considerations between the 3D and 2D models are also developed. Numerical results show that this model adaptive framework shows higher flexibility and compares well against finely resolved 3D simulations. In an actual application scenario, a 3 factor speed up is obtained, while maintaining the accuracy of the solution. • Novel notion of model adaptivity: governing equations are adaptively changed. • Coupling 3D Navier–Stokes and 2D thin film flow. • No a-priori information describing where to use which model. • Model and discretization changed on-the-fly. [ABSTRACT FROM AUTHOR]

Water entry of deformable bodies has been investigated extensively despite the major challenges in precise simulations of the whole physical process. Inspired by the basic idea of immersed boundary method (IBM), a hybrid FEM-IBM-level set algorithm is proposed where structural compliance is considered. The flow is described by Navier-Stokes equations with an added body force while the drastically moving object of arbitrary geometry is represented by several Lagrangian points on solid boundary. The direct forcing IBM is enhanced and coupled with finite element method (FEM) to facilitate simulation of severe fluid-structure interactions. Consequently, the added body force is calculated implicitly based on the exact velocity boundary condition with divergence-free condition ensured simultaneously. The improved conservative level set technique is adopted for accurate depiction of instantaneously distorted water surface, and the strongly coupled system is resolved iteratively through a partitioned scheme. Examples including sedimentation of a disk, water entry of deformable wedge and cylindrical shell are performed for validation. Specifically, hydroelastic impact of a three-dimensional conical shell is investigated, and the influence factors of entry dynamics are discussed. The results demonstrate the reliability and great potential of present algorithm for practical applications in ocean engineering, naval architecture and military engineering, etc. • Innovative algorithm for water entry of flexible body is presented. • Strong coupling effect among heterogeneous phases is achieved. • Mechanical behaviors of arbitrary shaped body could be reasonably reflected. • The influence factors of 3D water entry behaviors are revealed. • The versatile method enables precise simulations of practical hydroelastic problem. [ABSTRACT FROM AUTHOR]

We present a numerical model for the simulation of 3D sediment transport in a Newtonian flow with free surfaces. The Navier–Stokes equations are coupled with the transport, deposition, and resuspension of the particle concentrations, and a volume‐of‐fluid approach to track the free surface between water and air. The numerical method relies on operator splitting to decouple advection and diffusion phenomena, and a two‐grid method. An appropriate combination of characteristics, finite volumes, and finite elements methods is advocated. The numerical model is validated through comparisons with numerical experiments, sediment flushing, shear flow erosion, and the formation of dunes. [ABSTRACT FROM AUTHOR]

Catastrophic failures of partially or fully submerged structures, e.g., offshore platforms, hydrokinetic turbine blades, bridge decks, etc., due to the dynamic impact of free surface flows such as waves or floods have revealed the need to evaluate their reliability. In this respect, an accurate estimation of hydrodynamic forces and their relationship to instability in structures is required. The computational fluid dynamics (CFD) solver is known as a powerful tool to identify dynamic characteristics of flow; however, it commonly consumes a huge computational cost, especially in cases of re-simulations needed. In this paper, an efficient surrogate model based on the Gaussian process is developed to rapidly predict the nonlinear hydrodynamic pressure coefficients on submerged bodies near the water surface. For this purpose, a CFD model is first developed, which is based on a two-dimensional incompressible Navier–Stokes solver incorporating free surface treatment and turbulent flow models. Then, an experimental design is adopted to generate initial training samples considering the effect of the submerged body shape ratio and flow Re number. Surrogate models of hydrodynamic pressure coefficients and their instability based on Gaussian process modeling are established using the outcome from the CFD simulations, where optimal trend and correlation functions are also investigated. Once surrogate models are obtained, the mean and oscillation amplitudes of hydrodynamic pressure coefficients on a submerged rectangular body, which represents the shape of most civil structures, can be rapidly predicted without the attempt at re-simulation. The findings can be practically applied in rapidly assessing hydrodynamic forces and their instability of existing submerged civil structures or in designing new structures, where a suitable shape ratio should be adopted to avoid flow-induced instability of hydrodynamic forces. [ABSTRACT FROM AUTHOR]

In this paper we study the two-dimensional linear stability of a Papanastasiou fluid flowing down an inclined plane. The Papanastasiou constitutive law is a regularization of the Bingham law in which the singularity at zero strain rate is smoothed by an exponential function. The stability eigenvalue problem is solved by a spectral collocation method based on Chebyshev polynomials. We prove that, while the Bingham flow is unconditionally stable for every Reynolds number, the Papanastasiou flow becomes unstable at a critical Reynolds that depends on the material parameters, on the angle of inclination of the plane and on the prescribed inlet discharge. In particular, we show that the critical Reynolds is a decreasing function of the yield stress, showing the destabilizing effect of the yield stress. The results obtained her e show that the stability characteristics of a regularized flow can be extremely different from that of the exact Bingham fluid even if the two flows are "practically indistinguishable". • We study the motion of Papanastasiou fluid down an inclined plane. • We perform linear stability analysis of the basic 1D flow driven by gravity. • We obtain the eigenvalue problem which is nonlinear due to the free surface conditions. • We solve the problem numerically by means of spectral collocation method. • We discuss the results and we make comparison with the results obtained with the exact Bingham model. [ABSTRACT FROM AUTHOR]

This paper concerns the two-dimensional free surface cavity flow past an inclined plate in a finite depth. To close the cavity, a Riabouchinsky model is considered. The fluid is assumed to be inviscid and incompressible and the flow to be steady and irrotational. When the gravity and surface tension are negligible, an exact free streamline solution is derived. We solve the cavity flow problem by using two numerical methods. These methods allow us to compute solutions including the effects of gravity and surface tension. The first method is the series truncation and the second is the boundary integral equations, based on Cauchy integral formula. Numerical solutions are found for different values of the angle of inclination \gamma and for various values of the Weber number, the Froude number. Good agreement between the two numerical schemes and the exact solution provides a check on the numerical methods. [ABSTRACT FROM AUTHOR]

This paper outlines the implementation of an efficient implicit method for a free surface boundary for solving free surface flows with larger time steps. In this method, the governing equations are solved with dynamic conditions applied to the free surface boundary. The position and shape of the free surface are represented with adaptive boundary grid points. Unlike existing explicit methods, the proposed method solves the space conservation equation implicitly, making the calculations more stable and at a lower computational cost. The approach was implemented numerically by developing a new boundary field in OpenFOAM. Several test cases, including propagations of tidal wave, channel surge and solitary wave, were simulated to demonstrate the method's accuracy. The proposed method accurately predicted the first two cases using larger time steps. The Courant number of the solitary wave case should be less than 1 to reduce numerical errors, which would damp the wave amplitude. [ABSTRACT FROM AUTHOR]

Over the years, it has become obvious that simultaneous backfill grouting is of great significance to the design of the tunnel lining and process control of shield construction. It is essential to know the grout pressure distribution around the tunnel lining. The purpose of this study is to seek an alternative method to simulate the grout diffusion process and obtain pressure distribution of different time during simultaneous backfill grouting of tunnel construction. A lattice Boltzmann method (LBM) based free surface flow model is introduced and modified, and a Smagorinsky large-eddy simulation model serves to deal with the small-scale turbulent problem, which is a challenge for LBM to simulate the large-scale real-world engineering. The simulation results obtain the grout filling state with time and pressure distribution around the tunnel lining. Additionally, the grout pressures on site are measured at a ring in line 8 of Chengdu Rail tunnel, and the measurement results are also compared with ones taken from numerical simulation, it is showed that the numerical results are consistent with that of measurement on the whole. Through simulating different grouting strategies, it is concluded that for four-holes grouting schemes, the grouting pressures of upper holes are significant for the grout pressure distribution and should be paid most attention in construction. [ABSTRACT FROM AUTHOR]

As a typical meshless numerical method, Smoothed Particle Hydrodynamics (SPH) method has natural advantages in modeling free surface flows. However, this method is computationally heavy and time-consuming. Therefore, this paper proposes a SPH parallel algorithm based on particle decomposition. The algorithm distributes all particles to each process evenly for calculation, and the sending, receiving as well as broadcasting functions are called only once at each time step of communication, which is easy to implement and has good scalability. This parallel algorithm is used to carry out the numerical simulations of 2D dam-break flow and 3D droplet impact onto a liquid film. The results show that this SPH parallel algorithm can significantly reduce the simulation time and is conducive to 3D large-scale computation. The maximum speedup can reach more than 30 when the number of particles is greater than one million. [ABSTRACT FROM AUTHOR]

Flow caused by a line sink near a vertical wall in an otherwise stagnant fluid with a free surface is studied. A linear solution for small flow rates is obtained and a numerical method based on fundamental singularities techniques is applied to the full nonlinear problem. The sink is located at an arbitrary location away from all boundaries and the fluid is of finite depth. Steady solutions are presented for various flow rates and sink location. It is shown that the numerical results and linear solutions are in good agreement for small flow rates. The results suggest that steady nonlinear solutions are limited to flow rates below some critical value. Some interesting surface shapes are obtained depending on the location of the sink. [ABSTRACT FROM AUTHOR]

Thailand's beach had a severe coastal erosion problem at the end of rock dams called the "end effect". One of the innovative solutions to solve this problem is to use the derosion lattice (DL). However, since the DL performance depends on installing conditions such as angle of attack, placement position, terrain, and climate, computational fluid dynamics (CFD) was applied to assess the end effect's occurrence and optimize the performance of DL's installation. Based on Khao Rup Chang's condition, a suffered beach in Thailand was used as a case study, and a free surface flow simulation was performed in the transient state using ANSYS Fluent, a CFD software, which revealed water waves flow through the beach with and without the DL installation cases. Furthermore, the CFD-assessed results indicated that the angle of attack and placement position affected the DL performance as expected. In optimization, the 15° angle of attack with the DL placement adjacent to the rock dam was the proper condition. After being applied at the actual site, the DL can help reduce erosion, increase sedimentation, and solve the end effect with excellent performance. [ABSTRACT FROM AUTHOR]

The problem of two-dimensional free surface flow of inviscid and incompressible fluid over a step is considered. The flow is assumed to be as steady and irrotational, the effect of the surface tension is considered, but the gravity force is neglected. This problem is characterized by the nonlinear condition given by Bernoulli's equation on the unknown free surface, which can be considered as part of the solution. The main purpose of this work is to give an approximate solution of this problem, by using the Hilbert transformation and the perturbation technique; the results are calculated for a large values of the Weber number and small inclination angle of the step values. These results demonstrate that the used method is easily implemented, and provides approximate solutions to these kinds of problems.

The high-speed water entry dynamics and hydrodynamics of the projectiles are significantly influenced by the head shape and initial velocity. In this study, we numerically investigated unsteady cavitation dynamics during the water entry process and the hydrodynamic characteristics in the initial stages of conical, hemispherical, and blunt projectiles. We covered Froude numbers between 289 and 515, which are commonly handled in various industries. A preconditioned three-phase Navier–Stokes solver based on a homogeneous flow assumption was used for the numerical simulations. A dual-time stepping algorithm was applied to the current solver for physical time accuracy. The supercavitation regime under high-speed entry conditions with three projectiles is discussed, and the influence of the head shape on the pressure distribution, velocity, drag coefficient, and projectile shape is discussed in detail. Consequently, we suggest the physics of a high-speed water entry projectile based on the flow fields, cavitation dynamics, and time-dependent hydrodynamics under the effects of the projectile head shapes and initial velocity. • High-speed water entry dynamics under influence of projectile head shape and initial velocity were numerically investigated using a preconditioned 3D NS solver. • Froude number range of 289–515 is covered. • Unsteady cavitation dynamics on supercavitation regime near the projectiles were observed and discussed. • Hydrodynamics on initial stage of water entry such as free surface splashing, pressure distributions, drag coefficients were discussed. [ABSTRACT FROM AUTHOR]