Coupled nonlinear Schrödinger equations for interfacial fluids with a free surface

For interfacial fluids with a free surface, we derive a new system of coupled nonlinear Schrödinger equations in the small amplitude, quasimonochromatic limit. The derivation uses a recently derived nonlocal formulation of interfacial fluids bounded by a free surface.     

水中空气隔层衰减冲击波性能研究

 根据鱼雷对舰船毁伤的特点,建立了多介质水下爆炸数值模型,提出了交界面处理及广义光滑长度计算方法,编制了多介质水下爆炸计算程序,并对水下爆炸空气隔层衰减冲击波的性能进行了定量分析。结果表明：无论是接触爆炸还是非接触爆炸,空气隔层均可有效衰减冲击波,并且接触爆炸中空气隔层衰减冲击波的效果更好,最大可使冲击压力峰值降低约55%;空气隔层厚度与爆炸厚度之比为1时便可达到较好的衰减冲击波效果,继续增加空气隔层厚度对衰减冲击波效果影响不大。研究结果可为舰船结构防护及防雷舱的结构设计提供参考。     

A new kernel function for SPH with applications to free surface flows

Smoothed particle hydrodynamics (SPH) is a popular meshfree Lagrangian particle method, which uses a kernel function for numerical approximations. The kernel function is closely related to the computational accuracy and stability of the SPH method. In this paper, a new kernel function is proposed, which consists of two cosine functions and is referred to as double cosine kernel function. The newly proposed double cosine kernel function is sufficiently smooth, and is associated with an adjustable support domain. It also has smaller second order momentum, and therefore it can have better accuracy in terms of kernel approximation. SPH method with this double cosine kernel function is applied to simulate a dam-break flow and water entry of a horizontal circular cylinder. The obtained SPH results agree very well with the experimental results. The double cosine kernel function is also comparatively studied with two frequently used SPH kernel functions, Gaussian and cubic spline kernel functions.     

A critical investigation of smoothed particle hydrodynamics applied to problems with free‐surfaces

In this paper, an in‐depth study of SPH method, in its original weakly compressible version, is achieved on dedicated 2D and 3D free‐surface flow test cases. These rather critical prototype problems shall constitute suitable test cases to get through when building a free‐surface SPH model. The present work aims at investigating various numerical aspects of this method, often little mentioned in literature. In particular, a great care is paid to the dynamic part of the solution, which is critical to the local hydrodynamic load prediction. The role of numerical errors in the development of acoustic frequencies in the pressure signals is discussed, as well as the influence of the choice of the sound velocity. On the shown test problems, it is also evidenced that some numerical tools are crucial to ensure the robustness and accuracy of the standard SPH method. The convergence of our model is heuristically proved on these nonlinear prototype tests, showing at the same time the very satisfactory level of accuracy reached. Through these tests, some other numerical specificities of the SPH method are discussed, such as the self‐redistribution of the particles occurring during the Lagrangian evolution. A higher order model is also proposed, and its advantages and drawbacks are discussed. Copyright © 2013 John Wiley & Sons, Ltd.     

Large‐scale SPH simulations of droplet impact onto a liquid surface up to the consequent formation of Worthington jet

In this study, the whole process of liquid droplet impact onto a liquid surface up to the consequent formation of the central column was simulated using the smoothed particle hydrodynamics method (SPH), and compared with an experiment using a high‐speed video camera. The surface tension tensor for the particle‐based expression was adequately included as the gradient of the surface tension and that enabled the simulation leading to the formations of crater and crown as well as the consequent central column. The simulated time series of the crater depth and diameter and crown height corresponded quantitatively well with the experimental result up to the rebound motion while discrepancies remained as a lower central column height in the simulation, and this seemed to be ascribed to the difficulty in realizing the complex surface structure that inevitably appeared in the fast rebound motion. Copyright © 2009 John Wiley & Sons, Ltd.     

Global existence of strong solutions to the Cauchy problem for a 1D radiative gas

We consider a one-dimensional radiation hydrodynamics model in the case of the equilibrium diffusion approximation which is described by the compressible Navier-Stokes system with the additional terms in the pressure and internal energy respectively, which embody the effect of radiation. Under the physical growth conditions on the heat conductivity, we establish the existence and uniqueness of strong solutions to the Cauchy problem with large initial data, where the initial density and velocity may have differing constant states at infinity. Moreover, we show that if there is no vacuum in the initial density, then, the vacuum and concentration of the density will never occur in any finite time.     

An Euler system source term that develops prototype Z‐pinch implosions intended for the evaluation of shock‐hydro methods

In this paper, a phenomenological model for a magnetic drive source term for the momentum and total energy equations of the Euler system is described. This body force term is designed to produce a Z‐pinch like implosion that can be used in the development and evaluation of shock‐hydrodynamics algorithms that are intended to be used in Z‐pinch simulations. The model uses a J × B Lorentz force, motivated by a 0‐D analysis of a thin shell (or liner implosion), as a source term in the equations and allows for arbitrary current drives to be simulated. An extension that would include the multi‐physics aspects of a proposed combined radiation hydrodynamics (rad‐hydro) capability is also discussed. The specific class of prototype problems that are developed is intended to illustrate aspects of liner implosions into a near vacuum and with idealized pre‐fill plasma effects. In this work, a high‐resolution flux‐corrected‐transport method implemented on structured overlapping meshes is used to demonstrate the application of such a model to these idealized shock‐hydrodynamic studies. The presented results include an asymptotic solution based on a limiting‐case thin‐shell analytical approximation in both (x, y) and (r, z). Additionally, a set of more realistic implosion problems that include density profiles approximating plasma pre‐fill and a set of perturbed liner geometries that excite a hydro‐magnetic like Rayleigh–Taylor instability in the implosion dynamics are demonstrated. Finally, as a demonstration of including and evaluating multiphysics effects in the Euler system, a simple radiation model is included and self‐convergence results for two types of (r, z) implosions are presented. Copyright © 2008 John Wiley & Sons, Ltd.     

自由表面射流磁流体不稳定性分析(I)

利用微分解析方法分析了自由表面液态金属射流在非均匀的横向磁场中的稳定性行为，得出了在给定射流初始速度分布和磁场分布条件下，射流的速度空间分布表达式。在特定的条件下，射流存在固有稳定区，其稳定区长度与横向磁场的空间非均匀程度和射流的初始速度有关；但其向外溅射的位置与BT横向磁场的非均匀程度、射流的初始速度、液态金属粘滞系数和重力加速度有关。     

Vectorized multisite coding for hydrodynamic cellular automata

Simulating eight lattices for Pomeau's cellular automata simultaneously through bit-per-bit operations, a vectorized Fortran program reached 30 million updates per second and per Cray YMP processor. We give the full innermost loops.