随机脉冲微分方程的p阶矩稳定性和参激白噪声作用下Lorenz系统的脉冲同步

考察了随机脉冲微分系统的p阶矩稳定性问题,在更符合脉冲系统一般假设的情况下,建立了条件更弱的随机脉冲微分系统p阶矩稳定性判定定理.并应用该判定定理,考察了参激白噪声作用下Lorenz系统的脉冲同步问题,证明了同步误差系统的p阶矩稳定性,从而说明在p阶矩的意义下,两个系统是可以用脉冲方法实现同步的.数值模拟验证了随机Lorenz系统脉冲同步的可行性. 关键词： 随机脉冲微分方程 p阶矩稳定性')" href="#">p阶矩稳定性 脉冲 同步     

高精度非定常激波装配法

为正确模拟高超声速绕流中,来流小扰动与弓形激波之间的干扰对流动特征的影响,将弓形激波作为动边界,利用非定常特征关系处理激波处的边界条件.应用五阶精度迎风紧致格式和六阶精度的对称格式与三阶精度的R-K方法相结合,建立高精度非定常激波装配方法.采用该方法数值模拟钝锥高超声速定常流场和二维抛物外形高超声速边界层流动的感受性问题,数值模拟来流小扰动与弓形激波干扰激波后非定常扰动流场,研究扰动波进入边界层产生边界层不稳定波的特征.     

具有声激波的跨音流管道中声传播的数值方法

本文采用四阶MacCormack格式和附加四阶粘性项方法,求解具有声激波的跨音流变差分格壁管中的声传播问题,比前人结果有明显改善。本文详细介绍了这种差分方法,特别是关于截面硬式,人工粘性项和计算可靠性判据。这种方法省内存,省机时,可以在微机上实现计算。     

气相爆轰波在分叉管中传播现象的数值研究

数值研究气相爆轰波在分叉管中的传播现象.用二阶附加半隐龙格-库塔法和5阶WENO格式求解二维欧拉方程,用基元反应描述爆轰化学反应过程,得到了密度、压力、温度、典型组元质量分数场及数值胞格结构和爆轰波平均速度.结果表明:气相爆轰波在分叉管中传播,分叉口左尖点的稀疏波导致诱导激波后压力、温度急剧下降,诱导激波和化学反应区分离,爆轰波衰减为爆燃波(即爆轰熄灭).分离后的诱导激波在垂直支管右壁面反射,并导致二次起爆.畸变的诱导激波在水平和垂直支管中均发生马赫反射.分叉口上游均匀胞格区和分叉口附近大胞格区的边界不是直线,其起点通常位于分叉口左尖点上游或恰在左尖点.水平支管中马赫反射三波点迹线始于右尖点下游.分叉口左尖点附近的流场中出现了复杂的旋涡结构、未反应区及激波与旋涡作用.旋涡加速了未反应区的化学反应速率.反射激波与旋涡作用并使旋涡破碎.反射激波与未反应区作用,加速其反应消耗,并形成一个内嵌的射流.数值计算得到的波系演变和胞格结构与实验定性一致.     

间歇同步分数阶统一混沌系统

根据分数阶微分方程的性质,研究了间歇控制分数阶系统的稳定性,提出了间歇控制分数阶系统的一般理论并给出了数学证明. 根据该理论设计控制器实现了分数阶统一混沌系统的间歇同步, 数值仿真验证了该理论的正确性. 关键词： 分数阶 统一混沌系统 间歇同步 稳定性     

基于第二粘性的Navier-Stokes方程组求解正激波结构

为考察气体第二粘性（体积粘性）对正激波内部流动的影响机制，数值求解含第二粘性的一维Navier-Stokes方程组.结果表明：第二粘性对激波内部的密度、热流和能量分布等物理量具有抹平效应，导致热流和熵流的峰值减小、激波厚度增加，体积粘性耗散的增加使得一部分机械能转化为内能；考虑第二粘性所计算的密度分布和激波厚度大为改善，与实验数据吻合较好；当马赫数为1.2≤Ma≤10，激波内部的Knudsen数满足0.12≤Kn≤0.4，对于马赫数Ma≤4.0的激波内部流动，考虑第二粘性的连续流Navier-Stokes方程组能够准确地模拟正激波结构.     

激波作用不同椭圆氦气柱过程中流动混合研究

在激波与气柱相互作用问题中,压力与密度间断不平行产生的斜压涡量会引起流动的不稳定性,从而促进物质间的混合.本文基于双通量模型,结合五阶加权基本无振荡(WENO)格式,求解多组分二维Navier-Stokes方程,分析激波作用面积相同结构不同的椭圆气柱所致的流动和混合.数值结果清晰地显示了激波诱导Richtmyer-Meshkov不稳定性引起的气柱界面变形和波系演化.同时定量地从界面运动、界面结构参数变化(长度和高度)、气柱体积压缩率、环量及混合率等角度分析激波诱导的流动混合机制,研究椭圆几何构型对氦气混合过程的影响.结果表明,界面及相关参数的演化与气柱初始形状密切相关.当激波沿椭圆长轴作用于气柱时,气柱前端出现空气射流结构,且射流不断增长并渗透到下游界面,致使气柱分离成两个独立涡团,离心率越大,射流发展越快;同时激波作用气柱后在界面处产生不规则反射现象.圆形气柱界面演化与这种作用情形类似.当激波沿椭圆短轴作用于气柱时,界面上游出现类平面结构,随后平面上下缘处产生涡旋,主导流动发展,激波在界面作用产生规则反射,离心率越大,这些现象越明显.界面高度、长度、体积压缩率也因此有所差异.对界面演化、环量和混合率的综合分析表明,激波沿长轴作用于气柱且离心率较大时,流动发展较快,不稳定性导致的流动越复杂,越有利于氦气与环境介质的混合.     

拉氏数值模拟中的人工粘性方法

较好的人工粘性需要满足较小的计算开销、不能去除真实具有的涡运动等条件.提出一种应用于拉氏数值模拟中基于Lew人工粘性,同时增加了限制器的人工粘性方法.可以有效减少数值模拟结果对网格的依赖;采用特征值限制器控制施加的人工粘性大小,通过限制器能够区分激波压缩和等熵压缩;方便应用在二维、三维,结构网格或者非结构网格上.     

激波和火焰相互作用的数值模拟

本文应用基元反应模型和NND格式,数值研究了充满可燃预混气的二维管道中,激波和火焰的相互作用过程.计算中氢氧混合物的化学反应考虑了9种组分20个反应式,讨论了激波作用于火焰时,火焰的变化以及缓燃转爆震(DDT)的过程,分析了不同激波马赫数对激波和火焰作用过程的影响.结果表明:激波与火焰作用能触发爆震波的产生,爆震波是由管壁上形成的爆震中心引发.     

线性与非线性稳定性理论下液体射流空间发展的对比研究

分别基于线性和非线性稳定性理论,建立了描述同轴旋转可压缩气体中含空泡液体射流稳定性的一阶与二阶色散方程,并对色散方程进行验证分析;在此基础上,进行了射流表面一阶与二阶扰动及其发展的分析,线性与非线性稳定性理论下射流空间发展的对比研究.研究结果表明,二阶扰动波的波长和振幅明显小于一阶扰动波;沿射流方向,射流表面的扰动发展主要由一阶扰动波的发展所主导;随着轴向距离的增大,二阶扰动波才开始逐渐对扰动的发展起一定的作用.两种稳定性理论下射流表面的占优扰动模式不会发生改变;采用非线性稳定性理论时,可以反映一些实验中发现的射流表面出现"卫星液滴"的现象,由于考虑了射流表面的二阶扰动,射流界面振荡程度加剧.     

磁化尘埃等离子体中的冲击波及其横向扰动稳定性

利用双曲函数法得到ZKB方程的一组冲击波解,并对波在横向扰动下的动力学稳定性进行研究.对冲击波解进行线性稳定性分析,并构造高精度的有限差分格式求解所得本征值问题.结果表明：对于正耗散的情形,该冲击波在线性意义下稳定;对于负耗散情形,该冲击波在线性意义下不稳定.构造有限差分格式对受扰动的冲击波进行非线性动力学演化,结果表明：对于正耗散的情况,该冲击波是稳定的.     

On the viscous and inviscid stability of magnetohydrodynamic shock waves

We study the viscous and inviscid stability of shock waves in barotropic and full magnetohydrodynamics. We show that there are magnetohydrodynamic shock waves that are one-dimensionally stable as viscous shock profiles while they are multidimensionally strongly unstable as planar shock discontinuities.     

Viscous Shock Wave and Boundary Layer Solution to an Inflow Problem for Compressible Viscous Gas

The inflow problem for a one-dimensional compressible viscous gas on the half line (0,+) is investigated. The asymptotic stability on both the viscous shock wave and a superposition of the viscous shock wave and the boundary layer solution is established under some smallness conditions. The proofs are given by an elementary energy method.     

Stability of a Composite Wave of Two Viscous Shock Waves for the Full Compressible Navier-Stokes Equation

In this paper we investigate the asymptotic stability of a composite wave consisting of two viscous shock waves for the full compressible Navier-Stokes equation. By introducing a new linear diffusion wave special to this case, we successfully prove that if the strengths of the viscous shock waves are suitably small with same order and also the initial perturbations which are not necessarily of zero integral are suitably small, the unique global solution in time to the full compressible Navier-Stokes equation exists and asymptotically tends toward the corresponding composite wave whose shifts (in space) of two viscous shock waves are uniquely determined by the initial perturbations. We then apply the idea to study a half space problem for the full compressible Navier-Stokes equation and obtain a similar result. Research is supported in part by NSFC Grant No. 10471138, NSFC-NSAF Grant No. 10676037 and 973 project of China, Grant No. 2006CB805902, in part by Japan Society for the Promotion of Science, the Invitation Fellowship for Research in Japan (Short-Term). Research is supported in part by Grant-in-Aid for Scientific Research (B) 19340037, Japan.     

强脉冲激光在AZ31B镁合金中诱导冲击波的实验研究

为了研究强脉冲激光在镁合金中诱导冲击波的衰减,采用Nd:Glass脉冲激光(1054 nm,23 ns)对AZ31B变形镁合金试样表面进行冲击,并利用响应快、测量范围大的PVDF压电膜传感器以及示波器实时测量了强脉冲激光在镁合金靶中诱导激光冲击波的相对压力.根据冲击波每次在靶材背面反射时,所经过距离的不同得到激光冲击波在镁合金中的衰减规律.结果表明,在激光能量为5J的强脉冲激光作用下,镁合金中冲击波衰减的平均速度为5.83×10³ m/s,与镁合金中应力波纵波的传播速度相符;强脉冲激光诱导冲击波在镁合金中是以指数规律衰减的.试验所得分析结果对激光冲击强化镁合金的应用具有重要意义. 关键词： 激光 镁合金 压电膜传感器 衰减规律     

Behavior of viscous solutions in Lagrangian formulation

In this paper, the behavior of shock-capturing methods in Lagrangian coordinate is investigated. The relation between viscous shock and inviscid one is analyzed quantitatively, and the procedure of a viscous shock formation and propagation with a jump type initial data is described. In general, a viscous shock profile and a discontinuous one include different energy and momentum, and these discrepancies result in the generation of waves in all families when a single wave Riemann problem (shock or rarefaction) is solved. Employing this method, some anomalous behavior, such as, viscous shock interaction, shock passing through ununiform grids, postshock oscillations and lower density phenomenon is explained well. Using some classical schemes to solve the inviscid flow in Lagrangian coordinate may be not adequate enough to correctly describe flow motion in the discretized space. Partial discrepancies between von Neumann artificial viscosity method and Godunov method are exhibited. Some reviews are given to those methods which can ameliorate even eliminate entropy errors. A hybrid scheme based on the understanding to the behavior of viscous solution is proposed to suppress the overheating error.     

二维浅水波方程的数值激波不稳定性

研究二维浅水波方程的数值激波不稳定性问题.线性稳定性分析和数值实验表明,格式的临界稳定性与数值激波的不稳定现象有重要的联系.基于扰动量的增长矩阵分析,本文将高分辨率的数值格式和HLL格式进行特定的加权,设计一类新的混合型数值格式.其中可以调节非线性波速的HLLC与HLL的混合格式,数值试验展示了消除浅水波方程激波不稳定现象的有效性和鲁棒性.     

Stability of shock waves for the Broadwell equations

For the Broadwell model of the nonlinear Boltzmann equation, there are shock profile solutions, i.e. smooth traveling waves that connect two equilibrium states. For weak shock waves, we prove asymptotic (in time) stability with respect to small perturbations of the initial data. Following the work of Liu [7] on shock wave stability for viscous conservation laws, the method consists of analyzing the solution as the sum of a shock wave, a diffusive wave, a linear hyperbolic wave and an error term. The diffusive and linear hyperbolic waves are approximate solutions of the fluid dynamic equations corresponding to the Broadwell model. The error term is estimated using a variation of the energy estimates of Kawashima and Matsumura [6] and the characteristic energy method of Liu [7].Research supported by the Office of Naval Research through grant N00014-81-0002 and by the National Science Foundation through grant NSF-MCS-83-01260Research supported by the National Science Foundation through grant DMS-84-01355     

Three-Dimensional Lattice Boltzmann Model for High-Speed Compressible Flows

A highly efficient three-dimensional (3D) Lattice Boltzmann (LB) model for high-speed compressible flows is proposed. This model is developed from the original one by Kataoka and Tsutahara [Phys. Rev. E 69 (2004) 056702]. The convection term is discretized by the Non-oscillatory, containing No free parameters and Dissipative (NND) scheme, which effectively damps oscillations at discontinuities. To be more consistent with the kinetic theory of viscosity and to further improve the numerical stability, an additional dissipation term is introduced. Model parameters are chosen in such a way that the von Neumann stability criterion is satisfied. The new model isvalidated by well-known benchmarks, (i) Riemann problems, including the problem with Lax shock tube and a newly designed shock tube problem with high Mach number; (ii) reaction of shock wave on droplet or bubble. Good agreements are obtained between LB results and exact ones or previously reported solutions. The model is capable of simulating flows from subsonic to supersonic and capturing jumps resulted from shock waves.     

The refined inviscid stability condition and cellular instability of viscous shock waves

Combining the work of Serre and Zumbrun, Benzoni-Gavage, Serre, and Zumbrun, and Texier and Zumbrun, we propose as a mechanism for the onset of cellular instability of viscous shock and detonation waves in a finite-cross-section duct, the violation of the refined planar stability condition of Zumbrun-Serre, a viscous correction of the inviscid planar stability condition of Majda. More precisely, we show for a model problem involving flow in a rectangular duct with artificial periodic boundary conditions that transition to multidimensional instability through violation of the refined stability condition of planar viscous shock waves on the whole space generically implies for a duct of sufficiently large cross-section, a cascade of Hopf bifurcations involving more and more complicated cellular instabilities. The refined condition is numerically calculable as described by Benzoni-Gavage-Serre-Zumbrun.