Understanding the interaction between high-pressure bubbles and perforated multilayer structures is essential for evaluating structural damage in underwater explosion (UNDEX) scenarios. While previous studies have mostly focused on small-scale bubble dynamics near a single plate, the behavior of meter-scale UNDEX bubbles near multi-plate structures remains insufficiently explored, where buoyancy effect, structural configuration and interlayer media significantly influence the bubble dynamics. In this study, given the superior capability of the smoothed particle hydrodynamics (SPH) method in capturing heterogeneous interfaces, it is employed to investigate the bubble dynamics near a perforated double-plate structure. Firstly, the adopted SPH model is validated through the cases involving a high-pressure bubble in free field and a high-pressure bubble near a perforated plate, through comparisons with experimental snapshots. Subsequently, the dynamics of a large-scale UNDEX bubble near perforated double-plate structures are simulated, and the effects of key geometric and physical parameters, including the perforation diameter, the bubble-plate stand-off distance, and the interlayer medium, on the bubble motion modes and load characteristics are systematically investigated. The findings provide new insights into the interactions between UNDEX bubbles and multi-plate structures.

In this paper, a low-dissipation and accurate Riemann SPH is developed and applied to multiphase flows with large density ratios and strong shocks. To improve the accuracy of the pressure gradient approximation, the more accurate pressure differencing formulation (PDF) is adopted in the Riemann SPH framework, which allows obtaining smoother pressure and velocity fields. Furthermore, to mitigate the excessive numerical dissipation inherent in the Riemann SPH, a numerical limiter is embedded within the Riemann solver. Additionally, a renormalization operator associated with particle distributions is employed to achieve higher-order accuracy in kernel gradient computation, particularly when particles are disorderedly distributed. The accuracy and robustness of the improved SPH method are first validated by the benchmark test of the Sedov point-explosion with large discontinuities, demonstrating the model's advantage in capturing smooth velocity fields for light fluids. Subsequently, simulations of typical multiphase flow scenarios are conducted, and the SPH results are compared with reference solutions from other methods to showcase the accuracy and superiority of the proposed SPH approach. Finally, the applicability of the present model to three-dimensional cases is further verified through the simulation of 3D bubble oscillation, highlighting the effectiveness and necessity of both the limiter and renormalization operator in enhancing numerical accuracy and stability.

The two-bubble coupling dynamics near a boundary is always complicated due to the inter-bubble interaction and the boundary effect, and relevant research is still very limited. Benefit from the Lagrangian properties, smoothed particle hydrodynamics (SPH) has distinct superiority in handling the bubble fusion, tearing, and fragmentation. Using the SPH method, this work numerically simulates the nonlinear interactions of two large-scale underwater explosion bubbles near an upper wall and investigates the shock characteristics of the bubble pair. Given the superiority of Riemann solvers to handle discontinuities, an accurate multiphase Riemann-SPH method with the monotone upwind-centered scheme for conservation laws reconstruction is adopted. Through this method, the experiment of an out-of-phase bubble pair interaction near the wall is first modeled, and the reliability of the present model is proven by the comparison of the experimental data with the SPH results. Subsequently, the influence of several key factors, including the distance between the bubble pair (γbb), the distance from the bubble to the wall (γbw), and the phase difference of two bubbles (θ), on the dynamic bubble behavior, the jet mode, and the load characteristics are systematically discussed. In this study, four bubble jet patterns are discovered, namely, “merging-upward jet,” “merging-downward jet,” “upward-downward jet,” and “upward-counter jet.” Compared to the cases of θ = 0 and θ = 0.5, the bubble pair under θ = −0.5 always exerts a stronger impact on the wall regarding the pressure peak and impulse, with the upward-downward jet mode posing the greatest load to the wall.

In the present work, an accurate thermodynamic Riemann-SPH model for multiphase flows is developed. This model considers the effect of the thermal diffusivity ratio on the transient heat transfer, and more importantly, the Riemann approximation is introduced to deal with the discontinuous temperature field. Through several one-and two-dimensional heat conduction benchmarks, the accuracy and convergence of the developed model are firstly validated by comparing with the results of conventional SPH heat conduction models and analytical solutions. Subsequently, based on the developed SPH model and considering the heat-fluid coupling effect, several cases of rising bubbles are simulated, and the influence of the initial fluid temperature on the kinematic properties of the rising bubble is investigated. On this basis, the thermodynamic Riemann-SPH model is further refined by developing a thermal radiation SPH model and considering the effect of strong fluid compressibility on the temperature field. Finally, using the refined model, the oscillation of the cavitation bubble is simulated, and the heat conduction and radiation process is analyzed.

In this study, we systematically focus on the coupling mechanism between the free surface and array bubbles. The method of underwater electric discharge was utilized to synchronously generate the array bubbles. The current array design consists of three collinear bubbles arranged horizontally beneath the free surface. High-speed photography shows distinct bubble dynamics and water spike evolution patterns for different bubble-free surface stand-off distances of gamma(b) and gamma(f). Numerous distinct and novel phenomena were identified. Quantitative analyses are performed on the jet velocities of array bubbles and the width and rising velocity of the water spikes at different stand-off distances. It is shown that for small gamma(b) less than 1.0, the bubbles would merge as well as the water spike being formed. As gamma(b) increases, the integrated water spike is observed to be separated, resulting in three water spikes arising on the free surface. Rich shapes of water spikes with the required width or height can be produced by controlling the stand-off distances associated with the array bubbles. The findings can provide a probable reference for predicting dynamics of the water spikes caused by array oscillating bubbles.

Bubble oscillation and migration are complex dynamic processes that have been extensively studied for the applications of ocean engineering. However, the intricate coupling and interactions among various parameters that affect bubble oscillation and migration remain unclear. In particular, the correlation between bubble dynamics and abrupt alterations in the flow field is not defined. Here, based on a developed bubble dynamics model, a spatial-temporal correlation method was applied to bubble calculations to build quantitative correlations among the bubble deformation, motion and characteristic pressures for the first time. Subsequently, the sharp changes in the flow field caused by bubble oscillation and migration behaviours were further explored to reveal the fluctuating propagation mechanism and instability in the flow field. The results indicated that increasing water depth and initial static pressure, along with decreasing bubble equilibrium radius and initial oscillation velocity, led to a higher bubble oscillation frequency. However, these factors reduced the duration of each migration process, resulting in a smaller total migration. Surface tension stands out as the preeminent factor exerting influence on both the migration displacement and the velocity. In contrast, the bubble wall serves as the principal determinant for the migration acceleration. Furthermore, the propagation of bubble dynamics is influenced by the combined effects of bubble growth, collapse, and migration. Pressure propagation correlates most strongly with bubble radius, followed by migration velocity and acceleration, while other parameters exhibit weaker correlations with pressure. This study emphasizes the bubble interaction mechanism and propagation characteristics.

Smoothed Particle Hydrodynamics (SPH), a widely-used numerical method for simulating fluid flows with complex interfaces and boundaries, has undergone decades of development. This paper reviews the efforts towards advancing high-order SPH and its applications. The fundamentals of SPH are briefly introduced, followed by an analysis of errors arising in kernel and particle approximations. The relationship between consistency and accuracy is also discussed. To achieve high-order accuracy, this paper details three approaches: correcting SPH derivative operators, constructing kernel functions and implementing spatial reconstructions in the Riemann-SPH formulation. Finally, the applications of these high-accuracy SPH methods are described to show their potential for further development.

The interplay of coupling and entanglement among underwater bubbles exerts a pronounced impact on bubble dynamics, as well as the propagation characteristics of pulsations and velocities. Herein, both horizontal and vertical arrangements were considered. A double-bubble mathematical model was employed to emphasize the interactions between a pair of oscillating bubbles, with a single-bubble scenario serving as the control group. Spatiotemporal correlation analysis was conducted between the bubble motion patterns and flow-field instabilities. The results indicated that, within the double-bubble system, the predominant oscillation duration of the left-hand bubble was prolonged by over 50% in comparison to that of a single bubble. As the liquid level increased in depth, there was a notable delay in both the oscillation and migration of the bubbles, and the flow instability induced by the bubbles gradually diminished. Moreover, the acceleration of bubble oscillation and the viscous force emerge as the primary factors governing the momentum propagation. In contrast, the bubble radius and migration velocity exert only a negligible influence on the flow field. The current study provides new theoretical insights and quantitative tools for future research in multiphase flow and underwater bubble control strategies.

It is a notoriously challenge problem for Lagrangian particle methods to solve compressible flows with strong discontinuities and large volume variations. To overcome the problems of numerical oscillations, an accurate and stable Lagrangian Weighted-Least-Square (LWLS) method embedded with WENO-Z scheme (LWLS-WENO-Z) is proposed. To further enhance the numerical accuracy and stability, the particle shifting technique, the multi-level local-refinement technique, and the interface repulsive force are appropriately employed in the numerical scheme. Moreover, the smooth and stable coupled particle method between the LWLS and Roe's Riemann solver (LWLS-RR) is considered for the comparisons, further demonstrating the merit of the proposed LWLS-WENO-Z scheme. To reduce the simulation time, parallel computing with a CUDA-based program for the proposed scheme is implemented on a single GPU. In the numerical experiments, several 1D/2D benchmarks are solved to test the accuracy of the proposed method. Particularly, the challenge 2D underwater explosion and the cavitation bubble collapse and jetting are numerically investigated. Compared to other reference solutions, the present coupled particle method demonstrates robustness and superior accuracy in simulating these strongly-compressible multi-phase flows.

The acoustic cavitation oscillation behavior of a single bubble and the resulting characteristic pressure evolution is a complex dynamic phenomenon. The coupling mechanisms among many characteristic pressures that affect the oscillation characteristics are still ambiguous. A correlation method is applied to analyze the degree of correlation between characteristic pressures and bubble oscillations. The effects of ambient pressure, bubble state, and propagation of driving acoustic pressure on bubble oscillation and size were investigated. The results indicate that the viscosity is the dominant factor affecting bubble oscillating velocity during the growth or collapse processes. The surface tension is strongly correlated with the bubble oscillation, and the oscillating velocity of a bubble greatly suppresses the effect of the viscosity on the bubble oscillation. In particular, the sinusoidal variation in driving acoustic pressure strongly correlates with bubble radius oscillation, and its correlation with bubble acceleration increases linearly. Moreover, two linear relationships between the ambient pressure and the frequency to the characteristic radius are obtained.

The present work targets a high-order SPH scheme for simulating incompressible flows. To achieve this, typical spatial reconstructions, piecewise constant approximation, MUSCL, WENO and TENO techniques are employed in the Riemann-SPH formulation. These reconstructions are based on primitive variables rather than numerical fluxes, and the advection term is not altered. Therefore, the polynomial coefficients and the optimal weights in the W/TENO reconstruction are corrected to adapt this system. The accuracy of SPH is improved by W/TENO reconstruction up to 4th and 5th order in the Eulerian framework, respectively. The performances in the Lagrangian, ALE and Eulerian frameworks, and of different reconstructions are also compared. TENO-SPH can obtain comparable results with half (or even lower) of the particle resolution as compared to previous SPH versions. Moreover, the constraint of mass change related to the volume conservation and pressure instabilities is investigated in the Eulerian framework.

The present study aims to provide a deep understanding of curved wedge water entry. It involves a numerical simulation investigation into the kinematic and dynamic properties of water entry for two curved wedges with deadrise angles of 25° and 35°. The meshless Riemann-smoothed particle hydrodynamics (SPH) model embedded with an acoustic damper is developed to simulate these violent water entries. The validation of the Riemann-SPH accuracy is confirmed through comparison with experimental data, and subsequently, we make a systematical simulation study on curved wedge water entry, including a comparative study of free surface evolution and pressure distribution at different curvatures and drop heights. Furthermore, the kinematics analysis of velocity and displacement of curved wedges and time domain characteristics of slamming pressure loads on both sides of the wedge are investigated. It is revealed that the pressure distribution is symmetrical, with high-pressure regions forming near the bottom of the wedge and gradually propagating outward. The free surface profiles are symmetrical, with deeper depressions formed by sharper wedges. The entry depth and velocity are correlated with the initial theoretical entry velocity, and the rate of speed decline varies with the curvature of the wedge. The slamming pressure loads exhibit distinct time-domain patterns, with lower pressure loads by sharper wedges.

The impact of structure on water is an important and practical issue in ocean engineering. For some cases, the influence of air on the impact characteristics is non-negligible. In particular, when the flat-bottomed structure impacts on water such as the emergency landing on the water of an aircraft and helicopter, the air cushion will be formed which buffers the impact of the structure, thereby reducing its slamming load. In this paper, considering the advantages of the Riemann solver in dealing with discontinuities, a multiphase Riemann-SPH method using the PVRS Riemann solver is applied to analyze the air-cushion effect and slamming load in water entry problems. To reduce the numerical dissipation led by the Riemann solver, a dissipation limiter for the PVRS Riemann solver is given. Through the test of the water slamming of the plate, the accuracy and convergence of the adopted method are firstly validated. Then, the influences of the air cushion and the plate length on the slamming load are discussed. Finally, a complex engineering problem, i.e., the slamming of the LNG tank insulation panel is simulated, and the influences of the impact velocity and deadrise angle on slamming load characteristics are analyzed.

High-pressure bubble dynamics often involves many complex issues, including large deformations and inhomogeneities, strong compression, moving interfaces, and large discontinuities, that bring challenges to numerical simulations. In this work, an axisymmetric Riemann–smoothed particle hydrodynamics (SPH) method is used to simulate high-pressure bubbles near different boundaries. This Riemann–SPH can adopt the real sound speed instead of the artificial one for the air phase in the bubble. Therefore, the real compressibility of the air phase can be considered, and the corresponding time step is significantly increased. To avoid unphysical interface penetration and maintain relatively homogeneous particle distribution, a new and simple particle shifting scheme for multiphase flows is proposed. Additionally, to minimize the influence of the unphysical boundary on the bubble, a large fluid domain with an optimized initial particle distribution is adopted to reduce the particle number. Several high-pressure bubbles under different boundary conditions are considered, including in a free field, near a free surface, near a solid boundary, and near a rigid sphere. Numerical results show that these bubble dynamic behaviors can be reproduced with satisfactory accuracy.

In this paper, we developed an SPH scheme based on targeted essentially nonoscillatory (TENO) reconstruction. In this scheme, the Riemann-SPH method is applied to solve governing equations. However, the original Riemann-SPH generates excessive numerical dissipations due to the adoption of an approximate Riemann solver, thus exhibiting low numerical accuracy for simulating fluid flows. To solve this problem, we applied a five-point TENO method to reconstruct the left and right states of the Riemann problem. In the original TENO method, five equidistant stencil points are required. However, due to the nature of the Lagrangian-SPH method, the particle distribution is typically random. It is difficult for SPH to find equidistant points. To mitigate this issue, we first consider a particle pair as two stencil points and find the particle closest to the missing point. Through the gradient approximation, we can obtain the primitive values of the missing point. Based on these values, we can implement the TENO reconstruction smoothly. The excessive numerical dissipations are successfully reduced through TENO reconstruction, and the numerical accuracy is further improved. Importantly, the proposed TENO-SPH scheme avoids using the artificial viscosity commonly used in the conventional SPH. Moreover, TENO-SPH has a robust numerical ability, and thus, it can be applied to reproduce typical compressible flows, vortex flows, and free surface flows with superior accuracy.

近场水下爆炸涉及多相流体的掺杂耦合以及结构的大变形、损伤和断裂等瞬态强非线性现象,传统的网格算法在模拟近场水下爆炸时面临结构网格畸变、多相界面捕捉精度不足等难题,鉴于此,本文建立了完全无网格的近场水下爆炸冲击波和气泡全物理过程瞬态强非线性流固耦合动力学模型.流体采用基于黎曼求解器的光滑粒子流体动力学(SPH)方法求解,结构采用重构核粒子法(RKPM)求解,并基于法向通量边界条件实现流固耦合.为提高SPH对流场间断的求解精度,引入黎曼问题思想并结合MUSCL重构算法,为解决流场粒子体积变化剧烈导致的精度下降问题,应用了自适应粒子分割与合并方法.为模拟水下爆炸对结构造成的损伤断裂,基于退化实体几何表述,采用Lemaitre损伤算法,建立了 RKPM壳结构断裂损伤模型.依据所建立的SPH-RKPM流固耦合模型,对近场水下爆炸冲击波传播、气泡脉动与射流以及结构毁伤进行了模拟,将得到的冲击波载荷、气泡演化以及结构响应与实验值和其他数值解对比,验证了当前建立的SPH-RKPM流固耦合模型的有效性和精度,并给出了水下爆炸载荷特性及其对结构的流固耦合毁伤机制与规律,旨在为近场水下爆炸载荷预报提供理论和基础性技术支撑,为毁伤威力评估和舰船防护结构设计提供参考.

In this paper, we propose a targeted essentially non-oscillatory (TENO) SPH scheme. In this scheme, a 5-point stencil consisting of 3 candidate sub-stencils is adopted to implement the TENO reconstruction as originally proposed in the mesh-based methods. In the original TENO reconstruction, these five points are fixed and equidistant. However, it is difficult for SPH to determine these five points due to the random particle distribution. To remedy this issue, for two interacting particles, we first consider them as two existing stencil points. Then, for the other three points, we search for the closest particles to their exact positions. Subsequently, considering the gradient of these particles, we can finally obtain the values of these target points. Afterwards, the primitive values of points are reconstructed by TENO reconstruction where the polynomial interpolations are modified. Numerical results show that the proposed TENO-SPH scheme can be applied to reproduce some compressible flows involving shocks and small-scale structures, some incompressible vortex flows and free surface flows with superior accuracy.

The present work proposes a novel way of long-time accurate prediction of sea wave trains using the Long Short-Term Memory (LSTM) method. Typical kinds of regular waves (e.g. the Stokes wave), irregular waves (produced from the PM wave spectrum by either the equal frequency method or the equal energy method) and real sea wave trains are considered. The historical data of wave elevations are used in the training process of the LSTM model, based on which future wave evolutions are predicted. To improve the accuracy of long-time estimation of irregular waves, a multi-shot prediction method is proposed. The validity of the proposed approach is proved by comparing the performance of the single-shot prediction method and the multi-shot prediction method in multiple cases of irregular waves. In the meantime, the effects of the input and output lengths are investigated. Test results demonstrate that, although the standard LSTM scheme with the single-shot method presents appealing accuracy in forecasting regular waves, the multi-shot method is an essential component in enhancing the accuracy of long-time prediction of irregular waves.

A hydroelastic fluid–structure interaction (FSI) solver entirely based on the Riemann-SPH method is proposed. In this scheme, the Riemann-SPH method is incorporated to model elastic structures, which is performed by proposing a new treatment on Cauchy stress. The present structure solver can avoid the use of the artificial viscous force and can obtain good results. For the fluid, the conventional Riemann-SPH with a low-dissipation limiter is adopted to simulate incompressible free surface flows. The structure solver is coupled with the fluid solver by a simple coupling way considering the force balance. The developed structure solver is verified by three benchmarks, namely a free oscillating cantilever plate, stress concentration problem of a plate and wave propagation in a cable. Subsequently, through several 2D and 3D typical hydroelastic FSI tests, the accuracy and robustness of the present FSI solver are verified/validated by comparing with analytical solutions and experimental results.