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In this paper, a hybrid immersed smoothed point interpolation method (hybrid IS-PIM) is proposed, which employs a hybrid force approach to impose fluid-structure interaction (FSI) force condition. Compared with the original IS-PIM using a complete body force, the hybrid IS-PIM still utilizes the form of body force for pressure term to enhance the stability of numerical algorithm, and the shear force is applied to the boundary to accord with the physical law and the practical situation. Numerical examples have shown that the body force term enables the proposed method to overcome the constraint of mesh size ratio, and the boundary force term has a direct effect on the motion and deformation of solids, which yields more accurate results in comparison with the complete body force applied in the original IS-PIM. Moreover, the equivalence of FSI force in forms of body force and boundary force are also verified straightforwardly using a series of mesh combinations.

In this paper, a coupled scheme utilizing advantages of the Runge–Kutta discontinuous Galerkin (RKDG) method and finite elements is applied to investigate cavitation induced by rarefaction waves during a near-field underwater explosion of cylindrical charge. A high-order RKDG method has advantages of an accurate shock capturing. So, it was used to solve a governing Eulerian equation for a compressible fluid. A finite-element method (FEM) was suitable to deal with problems of a shock response of structures and, therefore, applied for structural analysis. The suggested method was used to study pressure characteristics and cavitation effects of underwater explosions of cylindrical charges near single/double plates. First, a cavitation model was introduced in the RKDG method, and a numerical model of a high-pressure bubble in a cylinder was developed. The obtained numerical results were compared with the known solution in order to verify the validity of the suggested method. Second, a RKDG-FEM model of underwater explosion of a spherical charge near a plate was developed; its results for maximum deflection at the centre of the plate were compared with experimental data to prove the effectiveness of the coupled algorithm. Then, this algorithm was employed to simulate the process of underwater explosions of cylindrical charges near a single plate. Here, effects of different parameters - thickness of the plate and a distance between the charge and the plate - on pressure and cavitation characteristics were studied. Finally, a numerical model of double plates subjected to a near-field underwater explosion was developed. Cavitation evolution and its effect on shock-wave loading were analysed. Additionally, the effect of the distance between two plates was studied. The suggested analysis and its results provide a reference for load characteristics of near-field underwater explosions and shock response of structures.

In this paper, the intense sloshing flow is simulated by Smoothed Particle Hydrodynamics (SPH) method successfully. First, the traditional SPH method is used for the simulation of sloshing process; and the obtained results for free surface shape and pressure evolution are in good agreement with the experimental data. Then, the δ-SPH method and particle shifting technique (PST) are introduced in the traditional SPH model to improve its stability and accuracy in simulating sloshing flow. Air phase does have an inescapable influence on water phase in intense sloshing process. Thus, an improved multiphase SPH model with pressure correction algorithm is utilized for interfacial sloshing simulation. The stability, accuracy and conservation of pressure correction algorithm are validated by the cases of hydrostatic test and dam breaking test. Besides, the comparison results show that unphysical pressure transmission at the interface between two fluids with large density ratio is effectively suppressed. Finally, the effect of air is considered in the multiphase flow simulation of sloshing process with presented multiphase δ-SPH and pressure correction utilized. The phenomenon that air phase is involved into inner water flow and then moves, rolls and rises in it is replicated accurately. It is found that both the shape of free surface and the air cavities during the slamming phase are well captured, which proves that the integrated multiphase SPH is effectively utilized for the simulation of such multiphase problem as sloshing.

Immersed smoothed point interpolation method (IS-PIM) was successfully proposed for solving fluid-structure interaction (FSI) problems with large solid deformations. However, the defects of IS-PIM include inaccurate solid boundary, spurious pressure oscillation and the “fresh node” phenomenon, which will cause different degrees of numerical errors. In order to solve these problems, the ghost-node immersed smoothed point interpolation method (Ghost-node-ISPIM) has been presented in this paper. In this method, the ghost-node technique is firstly proposed and achieved based on unstructured triangular elements, combined with mass source/sink algorithm and the sharp-interface method to fix the inherent defects existed in original IS-PIM. The effectiveness and superiority of the Ghost-node-ISPIM are demonstrated by a series of typical FSI numerical examples.

A process of target penetration by a shaped-charge jet includes three main stages: charge detonation, formation of a metallic jet and its penetration of the target. With continuously increasing computational power, a numerical approach gradually becomes more prominent (combined with experimental and theoretical methods) in investigations of performance of a shaped-charge jet and its target penetration. This paper presents a meshfree methodology - Smoothed Particle Hydrodynamics (SPH) - for a shaped charge penetrating underwater structures. First, a SPH model of a sphere impacting a plate is developed; its numerical results agree well with the experimental data, verifying the validity of the mentioned developed method. Then, results obtained for different cases - for various materials of explosives and liners - are discussed and compared, and as a result, more suitable parameters of the shaped charge in order to increase the penetration depth are obtained - HMX and copper were chosen respectively as the explosive and the liner material. It follows by validation of a model of a free-field underwater explosion, developed to verify the effectiveness of the modified SPH method in solving problems of underwater explosion; its numerical results are compared with an empirical formula. Finally, the SPH method is applied to simulate the entire process ranging from the detonation of the shaped charge to the target penetration employing the optimal parameters. A fluid around the shaped charge is included into analysis, and damage characteristics of the plate exposed to air and water on its back side are compared.

A shape of charge liners has a great effect on formation of a metal jet and its penetration into a target. In this paper, three different shapes of a charge liner, namely, conical, hemispherical and spherical-segment, are chosen to investigate their effect on damage response of a plate to underwater explosion. A Smooth Particle Hydrodynamic (SPH) method based on mesh-free Lagrange formulation is applied to simulate an entire process of a shaped-charge detonation, formation of a metal jet as well as penetration on a steel plate. Initially, a SPH model of the shaped charge with a spherical-segment liner is developed, and its results are compared with experimental data to verify the effectiveness of this method. Then, numerical simulations of shaped charges with different liners are performed to study the damage characteristics of a steel plate subjected to underwater-explosion shock loading and the metal jet. It was found that for the shock wave the peak value of the radial pressure is larger than that of the axial pressure during the detonation process; the level of pressure in the spherical-segment case was higher than that of the other two cases. After the detonation, the metal jet was gradually produced under the effect of the detonation wave. Three types of the metal jet - a shaped charge jet (SCJ), a jetting projectile charge (JPC) and an explosive formed projectile (EFP) – were formed corresponding to three cases with conical, hemispherical and spherical-segment liners. The obtained results show that the velocity and length of the SCJ in the conical case are greater than that of the other cases, and it therefore may lead to a larger penetration depth. In addition, the EFP has a better motion stability for a velocity difference in the spherical case is lower than that of the other two cases. Subsequently, the shock wave arrives at the plate earlier than the metal jet, which will cause deformation of the plate. Due to higher pressure, the shock wave in the spherical-segment case has a stronger damaging effect on the plate than that in the other two cases. Finally, the metal jet reaches the plate causing a hole. Because of a wider jet head, the EFP results in a more serious damage to the plate. The suggested analysis and its results provide a reference for structural design of shaped charge warheads.

In this work, the fluid–structure interaction (FSI) problems have been studied by coupling the δ Smoothed Particle Hydrodynamics ( δ SPH) with the Smoothed Point Interpolation Method (SPIM), which is abbreviated as δ SPH–SPIM coupled method. SPIM is used for structure dynamics owing to its good performance for large deformation analysis of solids. For the fluid solver, in order to further reduce the unphysical noise in pressure field, the δ SPH (where the density diffusion term is added into the continuity equation) is adopted. Inspired by the particle-element method, a new interpolation scheme is proposed for the coupling force calculation and transfer, which does not require the fluid and solid spacing to be the same. The coupled method has been verified by hydrostatic water column on an elastic plate, and has been applied to solve the problems of high speed water entry of an elastic wedge as well as dam-break flow.

Prediction of structural response during water entry is of great significance for the design of naval architecture and aircraft. In order to study fluid-structural interaction (FSI) of flexible wedge during water entry, coupling algorithms based on boundary element method (BEM)/Wagner theory and modal superposition method (MSM) are utilized. The first solution is a numerical method by coupling BEM and MSM based on domain decomposition technique. The second solution is a semi-analytical method by coupling Wagner theory and MSM. Non-linear pressure composition in the Bernoulli equation is used to improve the accuracy for wedge with moderate deadrise angles. The implicitly Newmark-β scheme is employed for time marching of structural dynamic equation. Effects of hydroelasticity on fluid pressure and structural response are studied by the comparison between coupling and decoupling solutions. The results show that the structural response is significantly affected by the presence of fluid added mass and damping. Structural response is lagged due to the fluid added mass and damping. Besides, the latter one causes the decrease of amplitudes of slamming load and structural response. This paper highlights the effect of hydroelasticity on slamming load and structural response during water entry of flexible structure.

A high-speed metal jet capable to cause severe damage to a double-hull structure can be produced after detonation of a shaped charge. A Smoothed Particle Hydrodynamics (SPH) method with a mesh-free and Lagrange formulations has natural advantages in solving extremely dynamic problems. Hence, it was used to simulate the formation process of a shaped-charge jet. A Finite Element Method (FEM) is suitable for a structural analysis and is highly efficient for simulations of a complex impact process in a relatively short time; therefore, it was applied to develop a double-hull model. In this paper, a hybrid algorithm fully utilizing advantages of both SPH and FEM is proposed to simulate a metal-jet penetration into a double hull made of different materials – steel and SPS (Sandwich Plate System). First, a SPH-FEM model of a sphere impacting a plate was developed, and its results were compared with experimental data to validate the suggested algorithm. Second, numerical models of steel/SPS double-hull subjected to a shaped-charge jet were developed and their results for jet formation, a penetration process and a damage response were analysed and compared. The obtained results show that the velocity of the metal jet tended to decrease from its tip to the tail during its formation process. The jet broke into separate fragments after the first steel shell was penetrated, causing the damage zone of the second shell that grew as a result of continuous impact by fragments. As for the SPS structure, its damage zone was smaller, and the jet trended to bend becoming thinner due to the resistance of the composite layer. It was found that the polyurethane layer could have a protective effect for the second shell.

High speed liquid jet and shockwave can be produced when a bubble collapses near a rigid wall, which may cause severe damage to solid structures. A hybrid algorithm was adopted to simulate bubble motion and associated pressures near a wall combining Level Set-Modified Ghost Fluid-Discontinuous Galerkin (LS-MGF-DG) method and boundary element method (BEM). Numerical results were compared with experimental data to validate the presented algorithm. Jet formation was simulated by BEM and the induced pressure on the wall was calculated with auxiliary function. The pressure at the point on the wall where the jet points to reaches its peak value after the jet penetrates the bubble. Bubble collapse and rebounding were simulated by the LS-MGF-DG method. Shock-wave is induced when the bubble collapse toroidally to a minimum volume and the pressure at wall center reaches the maximum due to shockwave superposition. A third pressure peak is found associated with the bubble rebounds and bubble splitting. In the case studied, a higher pressure was found due to collapse shockwave than bubble jet and affects a larger area of the wall. In addition, the three pressure peaks due to jet impact, collapse impact as well as bubble rebounding and splitting decrease with the increase of the standoff distance.

Damaged ship at sea will be a direct threat to lives and property, and it has a great significance of studying ship's remaining buoyancy, stability, sinking time and other important parameters. The process of a damaged ship sinking into water is a complex motion involving ship hull, inner and outer fluid coupled with waves and many other factors. It is featured by high nonlinearity and hard to establish a precise theoretical model to study. Yet SPH (smoothed particle hydrodynamics) as a meshfree method has a great advantage in solving such problems because of the nature of self-adaptive and Lagrangian. Firstly, the experiments of two scaled ship models with different openings sinking into water are carried out, through the sinking processes of broadside opening and bottom opening models, the conclusion is drawn that although the serious loss of stability of broadside opening model, the sinking time and other parameters are more conducive to rescue after maritime distress. Secondly, the parallel program of three dimensional SPH is developed to simulate the above more complex model, broadside opening model. The coupled process of sloshing is compared with that of experiment, and the results show good agreement with each other which verify the accuracy and feasibility of three dimensional parallel program.