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A consistent implicit Incompressible Smoothed Particle Hydrodynamics (ISPH) method based on projection approach is proposed for solving violent free surface flow problems. In this way, two consistent discretization schemes are employed for first and second spatial derivatives. In this study, it is shown that in explicit ISPH solvers, the field variables and the positions of particles in the process of numerical differentiation are estimated at two different time steps. So, the incompressibility is not completely satisfied. In the present approach, an iteration loop is implemented, in each time-step. Thus, at the end of each time-step both velocity and the positions used in divergence estimation are at the new time-level. The proposed ISPH method is validated in free surface flow problems involving 2-D dam break benchmarks in which both wet and dry beds are considered. Among the advantages of the present implicit method is being more accurate and stable than the explicit one, despite use of lower number of particles and greater time-step sizes. Also, it provides significant improvement in free surface simulations and pressure distribution results.

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Two incompressible SPH numerical solvers, including a modified explicit method and a new implicit method have been developed to simulate the sediment-laden free surface flow problems. Using, consistent discretization schemes, the proposed explicit method improves somewhat the accuracy of the usual explicit ISPH methods. The implicit method additionally guarantees the incompressibility condition completely. In the presented methods, the liquid phase is modeled using Navier-Stokes equations and to predict the non-Newtonian behavior of the sediment phase, the Bingham plastic rheological model is used. The accuracy and capabilities of the developed incompressible SPH methods is first validated in comparison with available experimental and numerical results of a single-phase water-sediment mixture flow generated by unsteady dam break problem. Then, they are applied to simulate an eroding dam break problem with a two-phase flow sediment transport. Comparing the obtained results with the available results in the literature shows that the developed methods particularly the implicit one, are very powerful tools for simulation of the problems including sediment transport induced by violent free surface flow, with interactions between flow and sediment and morphological changes in bed.

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Simulation of free surface flows using Weakly compressible moving-particle semi-implicit method Mesh-free particle (Lagrangian) methods, such as moving-particle semi-implicit (MPS) and smoothed particle hydrodynamics (SPH), are the newest methods in computational fluid dynamics, which have been applied in flow problems with large deformations and inconsistency. The aim of ths research was to develop and improve the simulation of free surface flows, using the new method of weakly compressible MPS (WC-MPS). In the MPS method, pressure is determined by solving Poisson equation. This equation is solved implicitly, which needs too much computer time. In the present research, the WC-MPS method is used to calculate pressure. In this method, as in SPH method, the state equation is used. This equation is solved explicitly, which does not occupy too much computer time. To evaluate the proposed method, the famous applied flow problem of dam break is analyzed. The program is written in C language and validations are performed for this code. To compare the Lagrangian approach with Eulerian approach, dam break is modeled by using FLOW-3D software too. The results of modeling approaches and physical models showed that both approaches have acceptable accuracy in modeling the free surface flow, but the accuracy of Lagrangian approach, especially the WC-MPS, is more than Eulerian approach. The proposed methos had some pressure oscillations, which were analyzed thereafter. Simulation of free surface flows using Weakly compressible moving-particle semi-implicit method Mesh-free particle (Lagrangian) methods, such as moving-particle semi-implicit (MPS) and smoothed particle hydrodynamics (SPH), are the newest methods in computational fluid dynamics, which have been applied in flow problems with large deformations and inconsistency. The aim of ths research was to develop and improve the simulation of free surface flows, using the new method of weakly compressible MPS (WC-MPS). In the MPS method, pressure is determined by solving Poisson equation. This equation is solved implicitly, which needs too much computer time. In the present research, the WC-MPS method is used to calculate pressure. In this method, as in SPH method, the state equation is used. This equation is solved explicitly, which does not occupy too much computer time. To evaluate the proposed method, the famous applied flow problem of dam break is analyzed. The program is written in C language and validations are performed for this code. To compare the Lagrangian approach with Eulerian approach, dam break is modeled by using FLOW-3D software too. The results of modeling approaches and physical models showed that both approaches have acceptable accuracy in modeling the free surface flow, but the accuracy of Lagrangian approach, especially the WC-MPS, is more than Eulerian approach. The proposed methos had some pressure oscillations, which were analyzed thereafter. Simulation of free surface flows using Weakly compressible moving-particle semi-implicit method

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In this paper, the dam break phenomena has been simulated in curved rivers using 3D numerical model, Flow-3D. It utilizes the finite volume scheme for structured meshes was used for solving the unsteady Reynolds-averaged Navier-Stokes equations in conjunction with the RNG k-ε closure model. In the utilized software, the Fractional Area/Volume Obstacle Representation (FAVOR) method is used to inspect the geometry in the finite volume mesh. FAVOR appoints the obstacles in a calculation cell with a factional value between 0 to 1 as obstacle fills in the cell. Fluid surface shape is illustrated by volume-of-fluid (VOF) function F(x,y,z,t). With the VOF method, grid cells are classified as empty, full, or partially filled with fluid. Cells are allocated in the fluid fraction varying from zero to one, depending on fluid quantity. The pressure and velocity are coupled implicitly by using the time-advanced pressures and time-advanced velocities in the momentum and continuity equations, respectively. FLOW3D solves these semi-implicit equations iteratively using relaxation techniques. In this paper the GMRES technique has been used as pressure implicit solver. A flux surface is a diagnostic feature in FLOW-3D for computing fluid flow rates. It can be used to obtain time-dependent information about the flow in different parts of the domain. A typical flux surface is a 100% porous baffle with no flow losses, so it does not affect the flow in any way. This feature gives the opportunity to determine the flood hydrograph at various stations downstream of the dam. Effects of curve angle and radious of curvature on the flood wave propagation and unsteady flow features along the curved reach, downstream of the dam has been investigated. Results showed that at the initial instants of the dam break in the straight channel, due to the effects of the dynamic wave, flood hydrographs at the dam location and at a distance downstream of the dam have local peak values, while in the curved chnnel cases, the flood wave becomes unstable immediately after the dam break and the local peak occures just at the dam section. The curved reach decelerate the flood wave propagation compared to the straight channel. Effect of channel curvature on the movement of the flood wave along the inner bank is higher than the outer bank and also the centerline of the curved channel. By decreasing the central radious of the bend, slope of the rising limb of the hydrograph and also the peak discharge, attenuates. Furthermore, the peak discharge time reduces. Unlike to effects of the curvature of the bend, increasing the bend angle does not affect the peak discharge. Changing the bend curvature and curve angle has no effect on the falling limb of the flood hydrograph at various stations downstream of the dam.

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The investigations of changes in bed surface of sediment due to the fluid flow and tracing sediment motion are complex and attractive for the researchers. In the recent decade, modeling of fluid flow using the Lagrangian methods, e.g. Smoothed Particle Hydrodynamics (SPH), is of interest. In this study, the open-source two dimensional SPHyiscs code is used to model the two phase Newtonian and non-Newtonian flows using the μ(I) visco-plastic model, which is obtained according to particle properties including inertia and friction coefficient. First, and in order to study the visco-plastic model, the one phase code is extended to non-Newtonian and the SPH results are compared with the experimental model of the collapsing granular column, where a harmonic interpolation is used for the viscosity of particles. In this stage, the comparison of the SPH model with the experimental data shows a good agreement. Then, the numerical method is utilized for the simulation of Newtonian dam-break fluid flow over a movable bed. The proposed model treat sediments as a non-Newtonian fluid using μ(I) model, by implementing the harmonic interpolation for the viscosity coupled with the Owen’s relation at the interface. Results show that the proposed model has a capability for simulating two-phase water sediment systems.

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Investigation of multi-physics problems such as flow-structure interaction (FSI) in free surface is very important in mechanical engineering, whereas numerical simulations of such problems have been widely conducted by researchers. The implementations of CFD in engineering applications are most of the time based on the Eulerian description. In this method, one can focus on flows at a fixed spatial point x at time t and any flow variable Φ is expressed as Φ (x, t). This description has been studied for over fifty years and is clearly understood. Most of commercial codes have been developed by using finite difference, finite element and finite volume approaches. Simulating free surface flow with most Eulerian CFD methods is potentially very difficult as explicit treatment of the free surface is required. Moreover, The problems of most Eulerian and mesh-based numerical methods for complex free surface deformations involves difficulties and complexities of various boundaries remeshing as well as moving boundaries and exact determination of free- surface fluid. Another description of study of CFD is the Lagrangian method where one can follow the history of an individual fluid parameter through the time. In the Lagrangian methods, any flow variable is expressed as Φ (x0, t), where the point vector x0 of the particle at the reference time t = 0. Smoothed Particle Hydrodynamics (SPH) is a meshless and fully Lagrangian method which is able to simulate the FSI problems due to its simplicity and capability, as there is no special treatment needed for the free surface. The current problem in hydrodynamic science and fluid engineering is studied as a complex phenomenon in free-surface flow. Smoothed Particle Hydrodynamics (SPH) is a flexible Lagrangian and meshless technique for CFD simulations initially developed by Lucy (1977) and Gingold and Monaghan (1977) to simulate the nonaxisymmetric phenomena in astrophysics. In recent years, the SPH method has been very popular in fluid mechanics, e.g. multiphase flows,3 heat conduction,4 underwater explosions, free-surface flows, etc. In this method, each particle carries an individual mass, position, velocity, internal energy and any other physical quantity. The Lagrangian nature of SPH would lead this method to be well suited to problems with large deformations and distorted free surfaces. Simplicity, robustness and relative accuracy in comparison with other numerical methods are the main advantages of using SPH.10 Moreover, the SPH method can handle fully nonlinear, multiply-connected free-surface problems and extend computations beyond wave breaking, which need complex treatments in other grid-based methods, e.g. Volume of Fluid (VoF).In this approach the computational domain is formed by a set of particles. Each particle represents macroscopic volume of fluid conveying information about the mass, density, pressure, speed, position and the other parameters related to the nature of the flow. However, the computational cost is a disadvantage of SPH because the time step is small because of the explicit integration scheme in a weakly compressible formulation. This method has been successfully applied to a range of free-surface problems which involve breaking and splashing up There is a choice of SPH formulation in the literature mostly expressed in weakly compressible forms where pressure is obtained from the equation of state In this research, SPH is used to investigate the flow-structure interaction in free surface. First, the simulation of dam break problem on a dry and infinite bed is shown and compared with the experimental data. Then, and after implementing the governing equations, the vibration of a beam is studied. Finally, the dam break problem on an elastic gate is shown. Comparison between the SPH results and available numerical and experimental data shows that the SPH method is useful method for simulating the FSI problem.