The boundary with an initial opening significantly affects shock wave propagation and bubble dynamics. To investigate the associated loading characteristics, this paper employs an axisymmetric Riemann-SPH method to simulate the shock wave and bubble near a single-layer deformable wall with an initial opening. The numerical model is first validated by simulating a spark-generated bubble experiment. Subsequently, the effects of plate deformation, opening radius, and stand-off distance on shock wave propagation, bubble pulsation, and jet evolution are systematically analyzed. The results show that plate deformation has little influence on shock wave propagation but significantly alters bubble pulsation and jet formation. At the opening center, the pressure history evolves from a double-peak to a single peak with increasing opening radius or stand-off distance. Bubble evolution presents three distinct jet modes: vertical jet, oblique jet tendency, and oblique jet. Small opening radii combined with short stand-off distances promote high-speed oblique jets and toroidal bubble formation, whereas increasing the stand-off distance weakens plate confinement, causing the bubble dynamics to gradually approach those in the free field. The study provides useful insight into shock wave propagation and bubble dynamics near non-intact plates and offers a reference for evaluating underwater explosion loading on damaged structures.

The underwater explosions of shaped charges generate metal jets, shock waves, and bubbles, which jointly cause localized perforation, large deformation, and tearing in structures. Nevertheless, the load evolution and associated damage mechanisms under different backing media remain insufficiently understood. Therefore, a comparative investigation of air-backed and water-backed plates subjected to underwater explosions of shaped charges is conducted through experiments and numerical simulations with smoothed particle hydrodynamics. The results demonstrate that the pronounced differences in density, compressibility, and acoustic impedance between air and water fundamentally alter the metal jet and bubble dynamics. Under air-backed conditions, the metal jet undergoes severe fragmentation. The bubble mixes with air and breaks up, preventing the formation of a bubble jet. For the structural response, the both plates undergo a "compression-rebound-compression" process, leading to a corrugated deformation in the air-backed plate. Quantitative analysis reveals that approximately 60% of the final hole size in the air-backed plate is attributed to the metal jet, while the remaining contribution mainly arises from bubble pulsation. Conversely, the metal jet plays a more dominant role in the penetration damage of the water-backed plate. The overall deflections for both plates are governed by bubbles, whereas the shock waves play a secondary role. These findings provide a reference for damage characteristics analysis of complex underwater structures.

Existing smoothed particle hydrodynamics (SPH) models struggle to capture the complete physical processes of underwater explosion (UNDEX), particularly the transition from shockwave propagation to cavitation bubble dynamics. This study develops a smooth-transition method between the Jones-Wilkins-Lee (JWL) and Ideal Gas equations of state (EoS), enabling consistent modeling of detonation product expansion, bubble growth, collapse, and jet formation while reasonably preserving system energy within acceptable numerical tolerances. Validation against analytical solutions (Geers-Hunter (GH) equation and Zhang equation) and eight experiments under free-field, free-surface, dual-charge, and complex-boundary conditions demonstrates the solver's stability, accuracy, and convergence. The proposed method overcomes limitations of conventional SPH models and provides a robust numerical framework for investigating UNDEX physics, with promising applications in marine engineering.

The metal jet formed by a conventional shaped charge has a high penetration depth but a narrow damage range. To expand the damage range of the metal jet, an annular shaped charge can be employed. In this paper, the underwater explosions of annular shaped charges are simulated by a graphic processing unit accelerated axisymmetric Riemann-SPH method, and the accuracy is verified by experiments. The hole-cutting effect using an annular shaped charge in an underwater explosion is analyzed, and the characteristics of the annular shaped charge are compared with a spherical segment shaped charge. Furthermore, the effects of the liner thickness on the annular jet are explored. It is revealed that the damage mode inflicted on the plate by an explosive formed projectile (EFP) is impact penetration, whereas that by an annular jet is cutting. The plate's breach size caused by the annular jet reaches 1.79 times the charge radius and 3.15 times that of EFP. Our findings also reveal that there is an optimal dimensionless maximum liner thickness lambda (lambda = T/Rz) to maximize the breach size dp, which is 0.12 for a charge mass of 60kg. This paper can provide support for the optimization design of the shaped charge.

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.

Strongly compressible multiphase flows, such as high-pressure bubble pulsations and jets, are typically characterized by complex interfaces with high density ratios, strong discontinuities, and long-term evolutions. As a result, traditional numerical methods often encounter significant challenges, including tracking multiphase interfaces, maintaining accuracy at discontinuous interfaces over long-term simulations, and enforcing physical non-reflection boundary. To address these issues, this paper introduces an adaptive SPH-FVM coupling model that integrates Riemann Smoothed Particle Hydrodynamics (Riemann-SPH) for computations within the core region, and Finite Volume Method (FVM) for calculations in other regions. It retains the benefits of the SPH method in handling large deformations and interface fragmentations, while leveraging the computational efficiency and boundary enforcement capabilities of the FVM method. This model is notably straightforward to implement and fully adaptive following initial setup. The predefined core particle region is adaptively adjusted, leading to a substantial reduction in the number of particles and an enhancement in overall computational efficiency. Furthermore, an optimized particle-mesh interpolation scheme (OPMIS) is proposed to handle the particle-mesh coupling at the interface, effectively mitigating numerical instability when high-pressure waves propagate from particles to meshes in shock problems. Additionally, the model is applied to simulate complex bubble behaviors in both free fields and near-wall boundaries. The numerical accuracy, efficiency, and robustness of the adaptive SPH-FVM model have been rigorously verified.

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 coupling effects and energy transfer mechanisms in multi-bubble systems have been long-standing focal points in fluid dynamics research. In this study, we theoretically investigate the dynamics of a spatial three-bubble system using a compressible bubble dynamics model that incorporates phase transition and migration effects. The dynamic behaviors and energy conversion processes are analyzed for different spatial configurations. Validation is performed through a series of spark-generated bubble experiments. Energy distribution and dissipation characteristics are compared across three experimental cases: two non-collinear arrangements with different initial dimensionless distances, and a linear arrangement. The results show that for bubbles positioned symmetrically, the interaction is governed by both dimensionless distance and arrangement shape. Furthermore, using a dimensionless framework, the effects of spatial configuration and flow field compressibility on system dynamics are examined. In particular, when the three bubbles are symmetrically arranged, fluid compressibility dominates the central bubble's energy dissipation.

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.

This paper comprehensively investigates the non-axisymmetric cavity dynamics of a vertically entering sphere under the influence of nearby side-walls through experimental, numerical, and theoretical analyses. Initially, we explore the characteristics of cavity evolutions with the sidewall effect. The emergence of a twin-vortex during cavity pinch-off is observed, and detailed numerical simulations provide insights into its underlying mechanisms. Both the dimensionless distance (λ) and the Froude number Fr significantly influence the pinch-off type. A phase diagram in the λ−Fr parameter space is presented, revealing the interplay between these variables. Moreover, we investigate the sidewall effect on the pinch-off time and location at low Froude numbers. The findings indicate that as λ decreases, both the pinch-off time and depth of the cavity increase. Generally, the wall effect is relatively weak when λ exceeds 4. Additionally, the pinch-off time can be described by τ=kr/g, with the constant k determined by λ. Utilizing 2D cavity theory, we estimate the pinch-off time of the water entry cavity with the sidewall effect, revealing a consistent collapse behavior with the mechanics of a two-dimensional cavity.

In some sea areas, the rising storm of bubbles including the release of large-scale methane gas and eruption of submarine volcanoes will pose a potential threat to the safety of ships. In the former case, a large amount of rising methane gas may generate some large-scale bubbles which may cause sailing ships to capsize. When the size of the bubble is close to the characteristic length of the ship, one single bubble could sink a ship. For the latter, the initial radii of the bubbles formed by the eruption of shallow seafloor volcanoes maybe tens even hundreds of meters, which also largely increases the risk of maritime transportation. In this paper, a 2D smoothed particle hydrodynamics (SPH) model is used to investigate the interaction between a ship and large-scale bubbles. Firstly, the adopted SPH model is validated by comparing with other numerical results. Then, the coupling interaction between a bubble and free-surface is simulated. Finally, under different conditions of different bubble sizes, bubble depths and horizontal distances, interactions between a ship and one or two large-scale rising bubbles are simulated and discussed, aiming to provide a reference for the investigation of ship capsizing caused by large-scale rising bubbles.

ObjectivesThis paper aims to address the numerical simulation problems of the dynamic response of ships subject to near-, medium- and far-field underwater explosions by establishing several numerical methods and calculation models. MethodsFirst, load and fluid-structure interaction models are established on the basis of the Eulerian finite element method and acoustic finite element method using the field-split technique, and FSLAB fluid-structure interaction software is developed. Next, near-, medium- and far-field underwater explosions are numerically simulated respectively. The shock wave propagation law, bubble shape and load evolution characteristics of near free-surface and near-wall underwater explosions are obtained, and the shock response characteristics of a spherical shell and ship subject to far-field underwater explosions are analyzed. Finally, the FSLAB software results are compared with the analytical solutions, reference solutions and experimental data. ResultsThe results show that the FSLAB fluid-structure interaction software developed in this paper is effective and accurate in simulating the impact damage of underwater explosions on warships. ConclusionThis study can provide a basis and support for the power assessment of underwater anti-explosion and shock design of warships.

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.