Violent Free Surface Flows Research Articles

Advances of the in-house developed SWLBM framework in simulating large-scale three-dimensional violent free surface flow with intense splashing

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.

Investigating landslide-induced tsunamis using a low-dissipation Riemann weakly compressible smoothed particle hydrodynamics model

In order to address the complex moving boundary problem and violent free-surface flows involved in the process of landslide tsunamis, this paper proposes a new low-dissipation Riemann-solver-based smoothed particle hydrodynamics (SPH) numerical model. In this model, the complex fluid-rigid slide interaction and friction effects on landslides are handled by an improved motion boundary approach based on a one-sided Riemann scheme. A weighted essentially non-oscillatory (WENO) reconstruction method is introduced to reduce excessive dissipation of the fluid caused by rigid landslide impact. The kernel gradient accuracy is assured by applying the corrected smoothed particle method (CSPM) into a continuity equation. Single-block and multi-block landslide tsunamis in two-dimensional (2D) or three-dimensional (3D) applications are simulated with different particle resolutions, and the results are compared to those of other numerical models and experimental results. The landslide trajectories obtained from the modified boundary model are in good agreements with the experimental values. Free-surface flows variations during the propagation are properly captured in the current simulations without introducing any artificial viscosity term, and the wave peaks exhibit deviations of −14%–10.5% from the experimental values, thus verifying the usability and robustness of the proposed Riemann-SPH model.

Volume conservation issue within SPH models for long-time simulations of violent free-surface flows

Smoothed Particle Hydrodynamics (SPH) simulations of violent sloshing flows characterized by a strong fragmentation of free-surface can be affected by volume conservation errors. These errors can accumulate in time and preclude the possibility of using such models for long-time simulations. In the present work, different techniques to measure directly the particles’ volumes by their positions are displayed. Thanks to these algorithms, we discussed how volume errors develop when introducing stabilization terms in the standard SPH schemes. Further, we show that the control of these errors can be achieved through two different (non-alternative) stabilization terms: (i) enforcement of dynamic boundary conditions on thin fluid jets and drops; and (ii) a dynamical switch that can impose or not the time variation of the particle masses.To demonstrate the effectiveness of the numerical techniques, four different violent sloshing flows are investigated and compared with experimental data.

A resolved SPH-DEM coupling method for analysing the interaction of polyhedral granular materials with fluid

Hybrid fluid–particle systems are prevalent in nature and engineering practices, but accurately simulating the dynamic behaviour is challenging due to their inherent strong non-linearity. This study proposes a three-dimensional resolved numerical framework for analysing complex shape polyhedron–fluid interaction. The weakly compressible smoothed particle hydrodynamics (SPH) is employed to describe the complex hydrodynamic behaviour, and the discrete element method (DEM) is applied to solve the motion of irregular polyhedral granular materials. An accurate contact collision algorithm is implemented in the coupling model to address the dynamic response of polyhedral particles. The high-fidelity modelling of the complex morphology of granular materials is realised. Hence, the coupling code is developed based on two high-performance open-source platforms, and an efficient two-way coupling scheme is designed to manage the fluid–particle interaction under a unified time framework. The reliability and the applicability of the SPH-DEM solver are demonstrated through extensive validations based on existing experimental and numerical data involving violent free-surface flow impacting multiple rigid bodies and cube deposition. Furthermore, a more complex case of wave-flow impact on rock piles is conducted, exhibiting great potential to employ this model in real-life engineering problems.

An efficient correction method in Riemann SPH for the simulation of general free surface flows

In this paper, a new efficient weighted correction method for weakly-compressible smoothed particle hydrodynamics is proposed and successfully implemented in the simulation of violent free-surface flow exhibiting breaking and impact events for the first time. It is well known that the original kernel gradient correction (KGC) encounters numerical instability resulting from matrix inversion. The present method remedies this issue by introducing a weighted average of the KGC matrix and the identity matrix, other than directly applying the KGC matrix, to achieve numerical stability meanwhile decrease numerical dissipation. To ensure momentum conservation, the correction is implemented in a particle-average pattern by rewriting the pressure term of the Riemann solution. Furthermore, the proposed weighted KGC scheme is incorporated into the dual-criteria time-stepping framework developed by Zhang et al. (2020) to achieve optimized computational efficiency. A set of numerical examples in both two- and three-dimensions are investigated to demonstrate that the present method can significantly reduce numerical dissipation meanwhile exhibit a smooth pressure field for general free-surface flows.

Development of Advective Dynamic Stabilization scheme for ISPH simulations of free-surface fluid flows

This study presents an enhanced version of a numerical stabilizing scheme, namely, the Dynamic Stabilization scheme (DS) by Tsuruta et al. (2013), referred to as the Advective DS scheme (ADS) for further enhancement of the numerical stability and accuracy in ISPH simulations of free-surface fluid flows. To ensure general stability of calculations, particle methods may benefit from particle regularization schemes including artificial repulsive force schemes to keep particles equally distanced. DS explicitly provides a stabilizing force based on the overlapped state of a target particle and its neighboring particle, resulting in a momentum-conservative repulsive force and stable simulations. However, DS may also result in numerical noises and numerical dissipation. Such numerical noises stem from the excess stabilizing forces because of consideration of the particle positions only. The approaching velocities of particles, corresponding to the divergence-free condition, are ignored. To precisely consider the dynamic states of particles in derivation of stabilizing forces, in ADS, the approaching velocities are additionally considered and the stabilizing forces are derived in a variationally consistent form based on time rate of particle overlapping state, to precisely recover the exact deteriorated particle regularity state. The enhanced performance of the proposed ADS scheme is shown through some benchmark tests including a Taylor-Green vortex, a dam break as a violent free-surface flow, an oscillating drop and a rotating square patch. The enhanced performance of ADS in terms of reproduced pressure and velocity fields, energy conservation and convergence are well demonstrated.

A numerical investigation on three-dimensional swirling instability in viscous sloshing flows

Resonant three-dimensional nonlinear sloshing in a square-base basin is analysed numerically to investigate swirling instability. The aim of this research is based on understanding how viscosity influences this instability. Four different fluids at increasing Reynolds number were considered in a tank forced to oscillate in a horizontal motion. The present study investigates the tight relation between the energy dissipation and this instability, showing that water tends to dissipate more energy during its rotating motion than the other three liquids characterised by higher viscosity. This aspect is strictly linked to the occurrence of free-surface fragmentation and liquid impacts. The numerical solutions are provided using an enhanced version of the Smoothed Particle Hydrodynamics (SPH) model called δ-LES-SPH model which proved to be suitable for the simulation of violent free-surface flows.

Numerical modeling of liquid spills from the damaged container and collision of two rising bubbles in partially filled enclosure using modified Volume-Of-Fluid (VOF) method

In the present work, two crucial shortcomings associated with Volume-Of-Fluid (VOF) model namely: (1) spurious interface smearing arising from false-diffusion errors, and (2) non-physical velocity fluctuation across the physical discontinuities, are systematically addressed, aiming to establish a unique methodological foundation and guidelines for the enhancement of interface-capturing techniques in handling multi-fluid flows. To accomplish this objective, first, a novel third-order bounded convection scheme is derived based on the Normalized Variable Diagram and Total Variation Diminishing concepts (NVD-TVD) and is then applied for the discretization of the volume-fraction equation. To cope with the instability issue induced by pressure fluctuation, the standard version of the implicit non-iterative PISO algorithm is first modified by incorporating the third pressure-correction step into the algorithm and is then utilized for the treatment of the pressure-velocity coupling. A feasibility and applicability of the proposed modifications in dealing with violent free-surface and multi-fluid flows are demonstrated against the five different challenging benchmark cases including two-dimensional dam-break flow over the dry bed, oil spill from the damaged container, single bubble rising, merging of two rising bubbles and two-fluid Rayleigh-Taylor Instability problems. The comparison of the obtained results with previously published literatures vividly corroborates the robustness and versatility of the modified VOF model in handling multi-fluid flows involving interface coalescence and breakup events. In the last staged, three new benchmark solutions namely (1) coalescence of two consecutive bubbles inside the partially filled enclosure, (2) two-dimensional three-fluid Rayleigh-Taylor Instability, and (3) oil/water spilling from the damaged tank are analyzed using the verified VOF method, aiming to provide a high-quality validation data for CFD simulations.

A CNN-supported Lagrangian ISPH model for free surface flow

As a popular method for modeling violent free surface flow, the incompressible Smoothed Particle Hydrodynamics (ISPH) based on the Lagrangian formulation has attracted a great attention worldwide. The Lagrangian ISPH solves the unsteady Navier-Stokes and continuity equations using the projection method, in which the pressure is obtained by solving the pressure Poisson's equation (PPE) that is the most time-consuming part in the ISPH procedure. In this paper, the Convolutional Neural Network (CNN) is combined with ISPH and used to predict the fluid pressure instead of solving the PPE directly. Although limited attempts of using CNN for solving the PPE in Eulerian formulation (referred to as the Eulerian CNN framework) in mesh-based methods are found in the public domain, the present model is the first ISPH model supported by CNN in a Lagrangian formulation. The proposed model overcome several challenges associated with combining CNN with ISPH, including selecting the input parameters, formulating the objective functions, producing the training dataset and dealing with boundary conditions. Two classic free surface problems, i.e. the dam breaking and the wave propagation, are simulated to evaluate the performance of the present model. Quantitative assessments of the numerical error in terms of both the free surface profile and the pressure field are carried out. The assessments show that the new model does not only give results with satisfactory accuracy, but also requires much less computation time for estimating pressure if the number of particles is large, e.g., 100 thousands particles that is usually required in the practical ISPH simulation for free surface flow.

Research on planing motion and stability of amphibious aircraft in waves based on cartesian grid finite difference method

The wave resistance of amphibious aircraft planing in waves is an important consideration in the design of seaplanes. Based on the Cartesian Grid Finite Difference Method (CGFDM), this paper investigates the effect of different wave elements and planing speeds on the motion response and vertical overload of amphibious aircraft, and analyzes the conditions for the occurrence of jump motion and stability of the aircraft. The finite difference method (FDM) based on a fixed regular cartesian grid system is used to solve the flow field, and the Tangent of Hyperbola for Interface Capturing with Slope Weighting (THINC/SW) method is used to capture the violent free surface flow, while the immersed boundary method (IBM) is used to effectively solve the problem of large motion of the object. The numerical simulation results are compared with the experimental values and show good agreement. The calculation results demonstrate that the heave and pitch motion responses of amphibious aircraft show a certain regularity with changing wave conditions. As the speed increases, the vertical overload rises sharply as the aircraft enters the complete planing state, and the slamming effect on the bottom of the aircraft's forward fuselage is most significant. When the wavelength reaches 1.38 to 2.76 times the length of the fuselage, high speeds and large wave steepness are more likely to induce jumping motions and reduce the stability of the aircraft's movement. This study can provide a reference basis for amphibious aircraft to effectively avoid unsafe sea state areas.

A coupled SPH-PD model for fluid–structure interaction in an irregular channel flow considering the structural failure

Understanding fluid–structure interaction (FSI) is important because it dominates diverse natural phenomena and engineering problems. This paper presents an integrated particle model for FSI problems involving irregular channel flows and crack propagation in structures. The proposed model is implemented as follows: (1) we couple weakly compressible smoothed particle hydrodynamics (WCSPH) with bond-based peridynamics (BBPD) in a partitioned approach (this framework has a much simpler algorithm than the previously reported SPH-PD method); (2) we propose a novel periodic boundary conditions (PBCs) algorithm for modeling flows in non-regular channels; and (3) we incorporate crack propagation in structural responses under fluid dynamics, which was rarely considered in previous works. The new framework has been validated and illustrated to be effective and versatile in diverse FSI problems, including hydrostatic pressure-induced solid deformation, violent free-surface flows and channel flows interacting with flexible structures. Compared with conventional grid-based methods, this particle framework is more user-friendly, since no extra effort is required to update meshes, even when a discontinuity appears during the modeling process. The extendibility and potential of this framework is further demonstrated by the simulation of fluid-driven deformation and crack propagation in elastomers.

Application of normalized SPH method to inviscid fluid flows with large deformation of free surface

A new normalized smoothed particle hydrodynamics (SPH) method has been presented recently and applied to transient solid mechanics problems of small deformation. The method can overcome boundary deficiency of the conventional SPH method without troublesome inversion of corrective matrix and provide convenience for treating boundary conditions. In this paper, a formulation of the normalized SPH method is derived for modeling inviscid fluid flows with large deformation of free surface. The treatment of dynamic free surface boundary conditions in the present method is addressed and theoretically compared with that in the conventional SPH method. A method based on kernel estimation is proposed for calculation of boundary summation and compared with the method based on α-shape. The normalized SPH method is applied to modeling inviscid free surface flows. Numerical results demonstrate that the present method is capable of modeling large deformation of free surface and can produce higher accuracy than the conventional SPH method, especially at boundary regions. The newly developed kernel estimation method for the calculation of boundary summation is more efficient than the α-shape-based method, and makes the computational efficiency of the normalized SPH method close to the conventional SPH method. To simulate violent free surface flows, a particle shifting technique is introduced in the present method. With this technique, the method is applied to simulating extremely large deformation, fragmentation and reconnection of free surface.

Breaking Solitary Wave Impact on a Vertical Seawall

Wave interactions with vertical and sloping seawalls are indeed complicated, especially for the impacts due to breaking waves, which are unsteady, turbulent and multi-phase. Available studies successfully measured the impact pressure due to waves acting on seawalls, whereas the associated flow velocity and turbulence characteristic received limited attention, indicating that the momentum of such violent free-surface flows cannot be determined. In this study, new experiments were carried out in a laboratory-scale wave flume using a non-intrusive image-based measuring technique (bubble image velocimetry, BIV) to measure the flow velocities due to a shoaling solitary wave impinging on and overtopping a vertical seawall. By varying the wave height of solitary waves, the breaking point of a shoaling wave can be changed. As such, the impact point of a breaking wave in relation to the seawall can be thereby adjusted. Considering the same still-water depth, two wave height conditions are studied so as to produce different levels of aerated flows. Effects of high- and low-aerated cases on free surface elevations, flow velocities and turbulence characteristics are presented so as to develop a better understanding of wave-structure interactions. More specifically, the maximum velocities and turbulence intensities at different evolutionary phases are identified for these two cases.

SPH method for long-time simulations of sloshing flows in LNG tanks

The present work is dedicated to the numerical investigation of sloshing flows inside a ship LNG fuel tank. Long time simulations, involving 3-hours real-time duration with realistic severe sea-state forcing, have been performed using a parallel CFD solver running for several weeks on a dedicated cluster. The numerical model adopted is the Smoothed Particle Hydrodynamics model (SPH). This model has been chosen for its Lagrangian approach and for the intrinsic properties of mass and momenta conservation which makes it well adapted for the simulation of violent free-surface flows. The adopted SPH method relies on a Riemann Solver for the calculation of the particle interactions which increases the stability of the scheme and allows for accurate predictions of the pressure during water impact stages. Three different filling height conditions are considered. For all of them energetic sloshing flows are induced with the occurrence of several water impact events. The latter are focused on specific zones of the tank depending on the considered filling height. For some conditions the SPH pressure predictions are compared with experimental ones. A critical discussion of these predictions is performed, highlighting the cases in which the numerical solver is able to provide good local pressure estimations.

Study on incompressible fluid analysis by three-dimensional particle method with finite volume techniques

Simulating violent free-surface flows by particle methods is effective. In recent years, the SPH (Smoothed Particle Hydrodynamics) method and the MPS(Moving Particle Simulation method) method are considered representative especially in the fields of ship engineering and civil engineering but these methods need various artificial parameters in calculation and may have unnatural large numerical oscillation in the calculated pressure values. In order to avoid these problems, the authors have proposed another particle method based on the finite volume techniques. The usefulness of the proposed method in two-dimensional problems has been verified by comparing the pressure fluctuation when a water tank of the two-dimensional model is forcibly oscillated with the corresponding experiment [1]. Therefore, in this research, the authors extended the algorithm so that the calculation formula can be applied to three-dimensional problems. The effectiveness of the calculation is demonstrated by applying to the dam break problem.

A numerical study on sloshing mitigation by vertical floating rigid baffle

Due to large hydrodynamic loads generated by the violent free surface flow, sloshing in partially filled tanks is an important phenomenon for the design of several offshore structures such as FPSO platforms, LNG carriers, crude oil carriers and, more recently, FLNGs. This study is focused on the numerical investigation of sloshing mitigation devices based on a floating baffle. For this purpose, the complex and highly nonlinear sloshing phenomenon is modeled and simulated using the Moving Particles Semi-Implicit (MPS) method, which is a fully-Lagrangian particle-based method for the simulation of incompressible flows widely applied to the study of fluid–structure interaction phenomena involving large free surface deformations, fragmentation and merging. As a reference for an in-depth discussion, the effectiveness of the equivalent fixed baffles placed at the bottom, the ceiling and mid-height of the tank were also studied. This work is divided into three parts: (1) the validation of the numerical method, (2) the study on the effect on sloshing of fixed baffles placed amid-tank and at different heights and (3) the investigation of the sloshing mitigation performance of floating baffles with a degree of freedom in the vertical direction of the tank. The effects of the floating baffles densities, which influence the draft of the baffles, on sloshing are investigated as well. The use of fixed baffles provided effective sloshing mitigation at the resonant frequencies for certain filling conditions depending upon the location of the baffle, but it might lead to even more violent flows in other filling conditions. On the other hand, the floating device presented sloshing mitigation for a larger range of filling conditions. Moreover, four different patterns of resonant motion of the floating baffle were identified and simple analytical estimations that could predict corresponding natural frequencies were proposed herein.

A generalized hybrid smoothed particle hydrodynamics–peridynamics algorithm with a novel Lagrangian mapping for solution and failure analysis of fluid–structure interaction problems

Fluid–structure interaction problems (FSI) are omnipresent in a wide variety of engineering fields and includes highly non-linear physics such as violent free-surface flow, complex interfacial and inter-phase interactions, and deformable structures with the possibility of damage formations. Well-established mesh dependent approaches may suffer from dynamic mesh-refinement, special algorithms to track free surfaces and handle the interface and inter-phase physics. On the other hand, due to their inherent nature, particle based meshless methods, namely Smoothed Particle Hydrodynamics (SPH) and Peridynamics (PD), can lend themselves easily to tackling with the above-stated complex physics involved in the fluid and structure phases of the FSI problems, respectively. This study presents a novel hybrid algorithm to couple the SPH and PD in a robust and high-fidelity manner for modeling extreme FSI problems with and without multi-scale defects. The coupled methodology is integrated with a novel mapping strategy based on Lagrange polynomial interpolation, which allows for the solution procedure to utilize different particle resolutions for fluid and deformable structural media. The mapping strategy enables one to construct a higher-accuracy PD solver that can predict the dynamic behavior of solids and provide an ability to model and track the damage nucleation, propagation, and branching in the structure phase of FSI domains. The corrected weakly compressible SPH is used for pressure–velocity coupling in the fluid phase whereas the ordinary state based PD is utilized for modeling the deformable structure. The SPH and PD solvers of the algorithm are validated separately through solving several well-accepted benchmark test cases such as the collapse of a water column, large deformation of a cantilever beam, and damage propagation in a plate under impact loading (Kalthoff–Winkler experiment). After validating each solver, the hybrid coupled SPH–PD algorithm is applied to simulate various extreme FSI problems of literature such as the dam break with an elastic gate, collapse of the water column and its hydrodynamic impact on an elastic obstacle, and the entry of a V-shaped deformable beam on the free surface of water in a tank. A close agreement between the SPH–PD results and the literature data is achieved for each of the aforementioned cases. The algorithm is further applied to model the failure propagation in the elastic wall of a tank under hydrostatic pressure. A realistic failure behavior is recorded for the FSI setups with different initial states of the wall, i.e., the wall is assumed to be with and without initial defects of different geometrical orientations. In particular, this study proposes and implements a new perspective for coupling different particle methods to achieve high-fidelity and low-cost modeling of complex FSI problems, which may involve multi-scale defects (i.e., cracks and voids) and failure propagations.

Numerical simulation of multiphase flows using an enhanced Volume-of-Fluid (VOF) method

The main objective of the present work is to enhance the stability and accuracy of Volume-of-Fluid (VOF) method for simulating multiphase flow problems with large density ratios and moving interfaces. In order to accomplish this, a novel high-order TVD flux-limiter scheme is developed and applied to approximate the convective fluxes in the momentum, energy and volume fraction equations. Moreover, the classical implicit non-iterative PISO algorithm is modified according to SIMPLER algorithm and the combined model (PISOR) is then employed to handle the pressure-velocity coupling. Furthermore, the piecewise linear interface calculation (PLIC) based on the Efficient Least Squares Volume-of-Fluid Interface Reconstruction Algorithm (ELVIRA) is adopted for the treatment of the interface and curvature estimation. The robustness and consistency of the proposed modifications in handling violent free-surface flows involving interface rupture and coalescence are verified via simulation of several canonical test cases including: dam break over the dry and wet beds, rotating square patch of fluid and Rayleigh-Taylor Instability (RTI). The results show that, the proposed flux-limiter scheme can significantly suppress false-diffusion errors and maintain interface sharpness while preserving the boundedness and positivity of the volume fraction field. Moreover, it is found that the proposed PISOR model has robust convergence behavior in strongly coupled multiphysics problems and provides more stable and consistent results than the standard PISO and SIMPLER algorithms. The performance and efficiency of proposed models are further verified, for single phase flow, through analysis of transient entropy generation due to natural convection heat transfer in differentially heated cavity.

Study of beach permeability's influence on solitary wave runup with ISPH method

Coastal protections, such as dykes, seawalls, breakwaters and natural beaches can often be considered as porous structures. The accurate prediction of wave motion around porous structures is necessary for the effective design of durable coastal protections. Smoothed particle hydrodynamics (SPH) is a meshless particle-based method suitable for the simulations of violent free-surface flows and their interaction with porous structures. In this paper, an incompressible SPH (ISPH) model is applied to the simulations of solitary wave runup on permeable slopes. The apparent density concept is introduced to allow the smooth particles’ volume to change when shifting between the pure-fluid region and porous region. The present simulations consider both the triangular beaches with uniform permeability and the solid beaches with overlying porous layers. The study focuses on the influence of permeability on the maximum wave runup heights. New runup laws are proposed, which offer guidelines for the design of porous coastal protections.

A CFD–FEA two-way coupling method for predicting ship wave loads and hydroelastic responses

This paper presents a co-simulation method for numerical prediction of nonlinear hydroelastic response of ship advancing in severe wave conditions. Two-way coupling of CFD and FEA solvers is applied where the external fluid pressure exported from the CFD simulation is used to derive the structural responses in the FEA solver and the structural deformations are fed back into the CFD solver to deform the mesh. Violent free surface flow such as slamming and green water on deck is well captured by the RANS and VOF techniques in the CFD solver. The nonlinear whipping and springing responses can be accurately simulated by the structural solver through the dynamic 3D FEA of the hull. By conducting co-simulations with a standard S175 containership, the developed fully coupled method was proved to be capable and reliable in accurate simulating almost all the physical characteristics of interests within the scope of ship seakeeping and hydroelasticity, which include large-amplitude motions, accelerations, wave loads, slamming loads, green water loads and whipping and springing responses of the hull in waves.