A Class of Planar Discrete Velocity Models for Gas Mixtures

We present a method for the construction of a simple class of physically acceptable planar discrete velocity models (DVMs) for binary gas mixtures. We want five conservation laws (no more, no less) with binary collisions. We first consider a collision with a particle at rest and different possibilities for the three other particles. We associate other particles and find semisymmetric qv _i models with q=7, 9, 11, 13 and 15, symmetric with respect to the two coordinate axes, but not to an exchange between the two axes. In order to avoid spurious mass conservation relations for the species without particle at rest, we find, for the two coordinate axes, that the tips of the momenta of the particles must be on two intervals parallel to one axis with opposite values on the other. There remain some physically acceptable q=9 (the smallest) and 11, 13, 15 models (adding multiple collisions for some others). Second, we construct the associated symmetric models qv _i^qv _i, which are superpositions of the qv _i model and another ^qv _i, rotated by /2. The possible previous defect of the spurious mass invariant for qv _i is transmitted to the symmetric one. We explain another defect coming from qv _i and ^qv _i having only one common particle, then spurious invariants exist for the momentum conservations along the two axes. We get four physically acceptable symmetric 17v _i (and three intermediate semisymmetric 13v _i models) and one 25v _i model superposition of two 11v _i and two 15v _i models (other acceptable symmetric 11v _i, 13v _i, and 25v _i models exist with multiple collisions).     

Hydrodynamic and Thermodynamic Nonequilibrium Effects around Shock Waves: Based on a Discrete Boltzmann Method

A shock wave that is characterized by sharp physical gradients always draws the medium out of equilibrium. In this work, both hydrodynamic and thermodynamic nonequilibrium effects around the shock wave are investigated using a discrete Boltzmann model. Via Chapman–Enskog analysis, the local equilibrium and nonequilibrium velocity distribution functions in one-, two-, and three-dimensional velocity space are recovered across the shock wave. Besides, the absolute and relative deviation degrees are defined in order to describe the departure of the fluid system from the equilibrium state. The local and global nonequilibrium effects, nonorganized energy, and nonorganized energy flux are also investigated. Moreover, the impacts of the relaxation frequency, Mach number, thermal conductivity, viscosity, and the specific heat ratio on the nonequilibrium behaviours around shock waves are studied. This work is helpful for a deeper understanding of the fine structures of shock wave and nonequilibrium statistical mechanics.     

Discrete Velocity Models Without Nonphysical Invariants

Models for mixtures of discrete velocity gases have been recently introduced by the authors and have produced unexpected results, particularly with regard to the possible existence of nonphysical collision invariants. Here we discuss a method to construct models without spurious invariants. The method can be extended to very general models, including polyatomic gases, chemical reactions, etc.     

Cu/PMMA复合材料的声速与冲击响应行为

基于熔融共混法,制备了一系列不同配比且随机分散的Cu/PMMA复合材料,重点研究了Cu颗粒含量对PMMA基体声速与冲击压缩行为的影响。超声测试结果表明,随着Cu颗粒含量的增加,声波的衰减使材料的横、纵波声速皆呈缓慢下降趋势,由此使体积声速亦呈减小趋势。基于平板撞击实验,获得了冲击压力在1.1~6.0 GPa范围内各复合材料的冲击波速度-粒子速度方程。Cu/PMMA复合材料声阻抗的升高使Hugoniot参数λ逐渐增大,而零压体积声速减小,与常压体积声速所表现出的变化趋势一致。结合已有的压力-粒子速度关系模型,对各材料的压力-粒子速度曲线进行了讨论。在此基础上,归纳出一种基于上述模型的用于预测金属粒子填充聚合物基复合材料压力-密度关系的可靠方法。     

孔隙率对铌硅粉末混合物冲击反应的影响

借助二级轻气炮加载平台和飞片撞击技术,在高冲击速度下实现不同初始孔隙率铌硅粉末混合物的冲击回收。对回收产物进行表征分析并探讨高冲击速度下孔隙率对铌硅粉末冲击化学反应的影响,实验结果表明:低孔隙率(10%)铌硅粉末混合物几乎不发生反应;20%孔隙率铌硅粉末发生不完全化学反应并生成了NbSi2;高孔隙率(35%)样品在相同冲击速度(飞片速度约为2.35 km/s)下发生完全反应获得单组分Nb5Si3。在高孔隙率的粉末混合物中,孔隙崩塌产生的高温是导致铌硅粉末反应物发生完全反应的主要原因。     

Discrete Velocity Models for Mixtures

Models of discrete velocity gases have been used for a long time, but only in the last few years have they become a tool to construct sequences converging to solutions of the Boltzmann equation. It appears that the case of mixtures has been rarely considered and only a couple of models, which are trivial in a sense to be explained in this paper, have been introduced. Here we thoroughly investigate the matter, and supply examples of models with both finitely and infinitely many velocities.     

Existence, Stability, and Convergence of Solutions of Discrete Velocity Models to the Boltzmann Equation

We prove the convergence of finite-difference approximations to solutions of the Boltzmann equation. An essential step is the proof of convergence of discrete approximations to the collision integral. This proof relies on our previous results on the consistency of this approximation. For the space-homogeneous problem we prove strong convergence of our discrete approximation to the strong solution of the Boltzmann equation. In the space-dependent case we prove weak convergence to DiPerna–Lions solutions.     

Newman-Penrose Formalism and Gravitational Impulsive and Shock Waves

Vacuum spacetimes endowed with two commuting spacelike Killing vector fields are considered. Subject to the hypothesis that there exists a shearfree null geodesic congruence orthogonal to the two-surface generated by the two commuting spacelike Killing vector fields,it is shown that, with a specific choice of null tetrad, the Newman-Penrose equations are reduced to an ordinary differential equation of Riccati type. fiom the consideration of this differential equation, exact solutions of the vacuum Einstein field equations with distribution valued Weyl curvature describing the propagation of gravitational impulsive and shock wave of variable polarization are then constructed.     

Discrete Velocity Fields with Explicitly Computable Lagrangian Law

We introduce a class of random velocity fields on the periodic lattice and in discrete time having a certain hidden Markov structure. The generalized Lagrangian velocity (the velocity field as viewed from the location of a single moving particle) has similar hidden Markov structure, and its law is found explicitly. Its rate of convergence to equilibrium is studied in small numerical examples and in rigorous results giving absolute and relative bounds on the size of the second–largest eigenvalue modulus. The effect of molecular diffusion on the rate of convergence is also investigated; in some cases it slows convergence to equilibrium. After repeating the velocity field periodically throughout the integer lattice, it is shown that, with the usual diffusive rescaling, the single–particle motion converges to Brownian motion in both compressible and incompressible cases. An exact formula for the effective diffusivity is given and numerical examples are shown.     

Periodic Waves of a Discrete Higher Order Nonlinear SchrSdinger Equation

The Hirota equation is a higher order extension of the nonlinear Schr6dinger equation by incorporating third order dispersion and one form of self steepening effect, New periodic waves for the discrete Hirota equation are given in terms of elliptic functions. The continuum limit converges to the analogous result for the continuous Hirota equation, while the long wave limit of these discrete periodic patterns reproduces the known resulr of the integrable Ablowitz-Ladik system.     

激波与火焰面相互作用数值模拟的GPU加速

为考察计算机图形处理器（GPU）在计算流体力学中的计算能力,采用基于CPU/GPU异构并行模式的方法对激波与火焰界面相互作用的典型可压缩反应流进行数值模拟,优化并行方案,考察不同网格精度对计算结果和计算加速性能的影响.结果表明,和传统的基于信息传递的MPI 8线程并行计算相比,GPU并行模拟结果与MPI并行模拟结果相同;两种计算方法的计算时间均随网格数量的增加呈线性增长趋势,但GPU的计算时间比MPI明显降低.当网格数量较小时（1.6×10⁴）,GPU计算得到的单个时间步长平均时间的加速比为8.6;随着网格数量的增加,GPU的加速比有所下降,但对较大规模的网格数量（4.2×10⁶）,GPU的加速比仍可达到5.9.基于GPU的异构并行加速算法为可压缩反应流的高分辨率大规模计算提供了较好的解决途径.     

纳秒激光冲击加载的全过程诊断

 与传统的冲击加载方式相比,激光驱动试样具有微尺寸（直径小于1 mm,厚度约10 μm）、超短作用过程（纳秒量级）等特点,但其速度变化历史的实时诊断颇为困难,因此发展适用于激光驱动的高时空分辨率的实时测试技术是十分重要和有价值的。采用桌面式脉冲Nd:YAG激光器作为加载平台,发展了激光加载下的小焦点多普勒光纤探针测量系统（焦斑直径约200 μm,时间分辨力约50 ps）,成功实现了从激光脉冲驱动微尺寸飞片飞行直至撞击Z-切石英试样的全过程实时诊断。实验结果显示,将6 μm 厚Al箔飞片驱动至2.48 km/s时,撞击Z-切石英试样的粒子速度为1.27 km/s,与Hugoniot理论计算结果相符,表明该测试技术是可靠、有效的;多层薄膜靶结构设计（基底/烧蚀层/硅油/Al箔）可提升激光与靶物质的能量耦合效率,使飞片保持更好的宏观完整性。为开展超短脉冲激光加载下材料动态特性研究提供了一种有效的技术途径。     

铁-铍介质界面上激波折射现象的数值研究

用数值方法研究铁-铍介质界面上的激波折射现象.运用激波极曲线理论分析不同强度的激波从正规折射过渡到非正规折射的临界角变化.运用一个具有二阶精度和波传播性质的激波捕捉法,数值求解激波折射运动的流体力学方程组.对正规折射,数值结果与激波极曲线理论一致;对非正规折射,不同强度的激波大都存在前驱的折射激波,并且入射激波的强度不同、入射角度不同,激波折射的图像也不同.     

铝阳极化冲击波探针的工艺探索

 为了在定形纯铝棒材（35 mm×Φ1.0 mm）上制取既薄、完整,又均匀、致密且电绝缘强度较高的绝缘膜,首先根据阳极化电解原理,测定了铝棒半球形端的极化曲线,获得了在50~60 ℃温度环境下铝绝缘膜稳定生长的区域在3~13 V之间这一重要的工艺条件;然后给出了铝电探针阳极化的步骤和相应的工艺参数。从而摸索出可批量生产适于液体冲击压缩实验的、性能一致性好、可靠性高的冲击波速度探测器的实验方法。同时,分析了电解系统温度条件以及沸水封孔工艺对强化铝绝缘膜的物理性质和电绝缘强度的影响。由此工艺可均匀地制得厚度在4~15 μm之间的Al₂O₃薄膜,在给定温度下制得平均厚度为6 μm的电探针耐直流电压为250 V、1 min,在液氮温度（77 K）下静置4 h后绝缘膜的物理外观和电绝缘强度都未发生变化。借助300 N·m冲击力发生器,测得该类探针的开关一致性不大于±20 ns。在较高冲击压力下,该特性有望得到进一步改善。     

PZT95/5粉体的冲击合成反应机理初探

 采用柱面冲击波回收装置，通过炸药爆轰产生的冲击波作用于Pb₄O₃、ZrO₂和TiO₂混合物粉体以合成PZT95/5粉体。通过对回收粉体进行的X射线衍射（XRD）分析，并结合冲击波理论，从实验和理论两个方面探讨了PZT粉体的合成机理和过程。结果表明，PZT的合成反应与Pb₃O₄的分解反应几乎同时进行，由于冲击波的特殊性，系统的温度和压力能同时满足Pb₃O₄分解和PZT合成的反应热力学条件，由Pb₃O₄分解的PbO一旦形成，就立刻与ZrO₂、TiO₂等氧化物反应生成PZT；冲击波合成PZT粉体属于特殊的固相反应，物质的扩散速度和反应速度大大提高。     

Propagation of Electron Acoustic Soliton,Periodic and Shock Waves in Dissipative Plasma with a q-Nonextensive Electron Velocity Distribution

The nonlinear properties of small amplitude electron-acoustic (EA) solitary and shock waves in a homogeneous system of unmagnetized collisionless plasma with nonextensive distribution for hot electrons have been investigated. A reductive perturbation method used to obtain the Kadomstev-Petviashvili-Burgers equation. Bifurcation analysis has been discussed for non-dissipative system in the absence of Burgers term and reveals different classes of the traveling wave solutions. The obtained solutions are related to periodic and soliton waves and their behavior are shown graphically. In the presence of the Burgers term, the EXP-function method is used to solve the Kadomstev-Petviashvili-Burgers equation and the obtained solution is related to shock wave. The obtained results may be helpful in better conception of waves propagation in various space plasma environments as well as in inertial confinement fusion laboratory plasmas.     

Velocity of a perturbation in infinite lattice systems

The problem of defining and estimating the velocity of disturbances in a crystal is investigated. Some results are given for plane rotors and anharmonic systems.Research partially supported by CNR.     

入射和反射激波诱导轻气泡变形和失稳的计算

采用NS方程对激波诱导球形轻气泡的变形失稳过程进行三维数值模拟,验证本文模型的可靠性,讨论气泡变形、涡环形成及其三维失稳过程.结果发现:球形轻气泡在入射和反射激波先后作用下,可以变形并沿流向形成多个旋转方向不同的涡环,而斜压效应是产生这些涡环的主要原因,涡环不仅在自诱导效应和流场作用下运动,而且自身会受到扰动而发生方位角不稳定.当涡环形成以小尺度流向涡为主的复杂结构时,即有可能诱发流场湍流化.     

Self-Similar Solution of Spherical Shock Wave Propagation in a Mixture of a Gas and Small Solid Particles with Increasing Energy under the Influence of Gravitational Field and Monochromatic Radiation

Similarity solution for a spherical shock wave with or without gravitational field in a dusty gas is studied under the action of monochromatic radiation. It is supposed that dusty gas be a mixture of perfect gas and micro solid particles. Equilibrium flow condition is supposed to be maintained and energy is varying which is continuously supplied by inner expanding surface. It is found that similarity solution exists under the constant initial density. The comparison between the solutions obtained in gravitating and non-gravitating medium is done. It is found that the shock strength increases with an increase in gravitational parameter or ratio of the density of solid particles to the initial density of the gas, whereas an increase in the radiation parameter has decaying effect on the shock waves.     

隔板深度对激波聚焦起爆影响的数值模拟研究

考虑几何结构参数对激波聚焦触发爆轰波的复杂影响,对H2/Air预混气的环形射流激波聚焦起爆现象开展了数值模拟研究,详细分析了不同隔板深度条件下的激波聚焦过程、流场演化特征以及爆轰波参数变化规律.研究结果表明,凹腔内激波聚焦诱导的局部爆炸以及隔板前缘处射流形成"卷吸涡"是引起爆轰波触发的两个重要机制,而隔板深度是影响环形...