Improved Method Of Smoothed Particle Hydrodynamics And Its Application To The Simulation Of Near-field Underwater Explosion

The near-field underwater explosion will not only lead to local damage to the structure of the warship,but also cause the entire warship to break and completely lose its combat capability.Therefore,the study of near-field underwater explosion is of great significance in naval architecture and marine engineering.Near-field underwater explosion is a process featured by high-speed,high-temperature,and high-pressure,often involving the doping and coupling of multiphase media,and it has strong nonlinearity and randomness.In recent years,with the rapid development of numerical methods,numerical simulation has become an important method for studying near-field underwater explosion.However,traditional mesh methods often face great difficulties in dealing with large fluid deformations and capturing heterogeneous interfaces.Therefore,more and more researchers have turned their attention to mesh-free methods.As one of the earliest and currently relatively mature meshless particle methods,the Smoothed Particle Hydrodynamics(SPH)method has been widely used in many engineering fields and has achieved fruitful results.Thanks to its Lagrangian characteristics,when simulating underwater explosions,the SPH method will not be troubled by grid distortion and can automatically capture mulphase interfaces,greatly reducing the complexity of numerical algorithms,and therefore has great advantages over traditional mesh-based methods.However,the conventional SPH method often faces some challenges in terms of numerical accuracy and efficiency when simulating near-field underwater explosions.In response to these problems,this paper proposes an improved high-precision SPH numerical model suitable for the simulation of near-field underwater explosions.The near-field underwater explosion problems,including shock wave,bubble pulsation and jet flow,as well as the structural damage caused by underwater explosions,are simulated by the present SPH model,aiming at providing a stable and reliable numerical method for the simulation of near-field underwater explosion.The basic concepts of the SPH method are firstly introduced,the discrete SPH Euler equations are given and several commonly used state equations are introduced.After that,the solid boundary conditions in the SPH method are given,and a high-precision non-reflective boundary condition suitable for high-speed impact problems is proposed based on the method of characteristics using time-line interpolations.Then,the Riemann idea is presented and introduced into the SPH method to form a Riemann SPH method suitable for dealing with discontinuous problems.Finally,in order to correct the impact of particle inhomogeneity on accuracy in the problem of strong compressible multiphase flow,an improved multiphase flow shifting algorithm is proposed.For the capture of near-field underwater explosion shock waves,a high-precision Riemann SPH numerical model suitable for shock capture is proposed.This model is based on a new WENO reconstruction scheme under the SPH framework.It reconstructs the physical quantity of the template point by searching for the particles closest to the stencil points and applying Taylor expansion to overcome the missing of the stencil points caused by the irregular distribution of particles in the SPH method.The convergence of the WENO-SPH method is studied through the gradient reconstruction of a simple function,and the accuracy is verified by a number of benchmark examples.The proposed WENO-SPH method is used to simulate two-dimensional and three-dimensional underwater explosions,and the results are compared with the empirical solutions.The influence of different Riemann solvers and reconstruction methods on the accuracy of shock wave capture are investigated.Finally,the Schmidt cavitation model is introduced into the SPH method to simulate the cavitation phenomenon in the nearfield underwater explosion.The proposed adaptive Riemann SPH model is used to simulate underwater explosion bubbles under different boundary conditions such as free field,near free surface,near wall surface and rigid suspended sphere,and the SPH results are compared with empirical solutions,other numerical results and experimental data.For the bubble pulsation and jetting produced by the near-field underwater explosion,an adaptive Riemann SPH method suitable for the simulation of large-density and strong compressible multiphase flow is proposed.Compared with the traditional multiphase SPH method using artificial viscous force,the advantage of Riemann SPH is that when dealing with the water-gas multiphase flow involving a large density ratio,the real sound speed can be used for the gas phase instead of the artificial sound velocity in the traditional SPH method.Therefore,Riemann SPH can consider the true compressibility of the gas phase,and more important,the corresponding time step will also be significantly increased.In order to reduce the volume variation of particles in the bubble pulsation process,an adaptive particle splitting and merging algorithm is adopted.To ensure the uniform particle distribution during the simulation,a simple and effective multiphase flow shifting technique is proposed.In order to reduce the influence of boundary reflection on bubbles,a non-reflective boundary condition is adopted.To reduce the number of particles required,an initial gradually spatially varying particle resolution is used.Applying the proposed adaptive Riemann SPH method,several highpressure bubbles under different boundary conditions including in the free field,near free surface,solid wall and a rigid suspended sphere are simulated,and the SPH results are compared with empirical solutions,experimental data and other numerical results.For the shell structure in the near-field underwater explosion,based on the classic MindlinReissener shell theory,the FPM method is used to establish an elastoplastic shell model.Compared with the traditional SPH method,the FPM method has higher accuracy in dealing with boundary truncation and uneven particle distribution.By simulating the elastoplastic response of circular flat plate and spherical shell under constant load and shock load,the accuracy of the established elastoplastic shell model is verified.For the simulation of structure damage caused by the near-field underwater explosion,a new fluid-structure coupling SPH algorithm under the axisymmetric framework is proposed.The algorithm is established based on the normal flux boundary condition.The single-layer shell particles are projected onto the axisymmetric plane as the boundary of fluid particles,and the fluid load on the structure particles is obtained by interpolation.The fluid-structure coupling algorithm is used to simulate the damage of simple shell structures including flat plates cylindrical shell and spherical shell by underwater contact explosions and near-field underwater explosions,and the response characteristics of different structural forms are explored.In addition,based on the axisymmetric Riemann SPH method,the damage of the plate caused by jet produced by the underwater explosion of shaped charge is simulated.