绝热流Chaplygin气体的Riemann问题

本文研究了绝热流Chaplygin气体动力学方程组,利用特征分析方法,在得到所有基本波的基础上,构造出Riemann问题的所有解.Riemann解由前向疏散波(激波)、后向疏散波(激波)、接触间断以及δ波构成.     

Chaplygin气体Euler方程组Riemann问题解的结构稳定性（英文）

研究了Chaplygin气体Euler方程组Riemann解的结构稳定性.当修正Chaplygin气体的压力趋于Chaplygin气体压力时,可压Euler方程组Riemann解的结构是稳定的.特别地,当修正Chaplygin气体的压力趋于Chaplygin气体压力时,Chaplygin气体Euler方程组Riemann问题的δ激波解是由后向激波和前向激波形成的Riemann解的极限.     

开闭磁场位形中慢激波的传播 *

用一个二维MHD数值模型 ,数值模拟研究了慢激波在近太阳子午面内开磁场和闭磁场中的传播 .结果表明 :开磁场中的慢激波可以保持其慢激波的特性传向行星际空间 ,但闭场中的慢激波在通过盔形电流片向开放形磁场传播时可以转化为中间激波 .     

三个自变量下强间断相互作用的精确计算

本文提出了能精确计算三个自变量下双曲型方程组强间断相互作用的比较完整的方法,给出了三维定常流中激波与激波的相互作用、激波与切向间断的相互作用的一些计算结果.另外还提出了一种基于特征理论的能自动精确确定嵌入激波的方法.给出了定常流中悬挂激波的计算结果.     

一种在双驱动激波管和激波风洞中实现运动激波与头激波斜相互作用的新方法

本文在讨论和分析了国外现有的运动激波与头激波斜相互作用的两大类实验方案的基础上,提出并实现了在双驱动激波管和激波风洞中形成运动激波与头激波斜相互作用的新方法.这种方法不仅可以获得双波(指运动激波与头激波,下同.)斜相互作用所需要的平面的运动激波,而且可以同时得到双波斜相互作用条件下试验模型表面瞬态压力曲线和流场照片.这种方法还可以用于研究在运动激波前有气流情况下,运动激波在尖劈或尖锥表面规则反射(Regular Reflection)与Mach反射(Mach Reflection)之间的转变.在测试技术方面,本文还提出了一种改进方法,用于测量运动激波的激波Mach数.     

一种新型的用于激波折射、绕射和干扰研究的组合设备

本文介绍一种新型的激波风洞-激波管组合设备。作为它的应用,文中还给出了在常规设备上所难以进行的三项实验:“运动激波在射流边界上的折射”,“波前有流动情况下的激波绕射”和“运动激波-头激波干扰”,并对所观察到的一些新的现象进行了分析和讨论。     

菱形口射流与超音主流的相互作用

基于在不同射流角(10°, 27.5°, 45°, 90°)和射流总压(0.1 MPa, 0.46 MPa)下,对音速次膨胀射流通过菱形口喷射到马赫5横穿主流的实验及圆形射流器的对比实验,研究了次膨胀射流与超音横穿主流相互作用流场, 实验包括横截面流场的Pitot和锥静压力, 获得横截面马赫数、 压力分布．结果表明近壁面低马赫数半圆区为尾区,尾区附近边界层减薄．脱体激波高度向自由流扩展,激波形状更弯曲, 低马赫数区较大．高射流压力和射流角增加羽流涡度,激波位置较高．90°菱形和圆形喷射器有更强的羽流涡度,但圆形喷射器的低马赫数区较小．前沿渐细的变壁面的斜面物增加羽流涡度,反之,双变壁面的斜面物减弱羽流涡度．通过表面激波形状、中心平面激波及横截面激波模化三维激波形状,激波总压损失用正激波关系式通过马赫数法向分量估计．激波总压损失随射流角和动压比的减小而减小,最大损失发生在90°圆形和菱形喷射器．     

管道内激波的不稳定性

本文将无限大激波阵面的激波不稳定性理论[1]推广到矩形截面管道内的激波不稳定性问题.首先,给出这个问题的数学提法,包括扰动方程与三类边界条件.其次,给出扰动方程的普遍解.上游和下游的普遍解分别含有5个待定常数.再次,在一类边界条件和一个假定下,证明了激波前扰动为0,激波后两个声扰动之一为0.边界条件是,X→±∞处扰动物理量为0.假定只讨论激波不稳定性问题,从而可先设ω=iγ,γ是不稳定性增长率,为正实数.另一类边界条件是管壁上法向速度扰动为0,它使波数只能取一组离散值.最后,用扰动激波上的5个守恒方程这一边界条件来决定激波后4个待定常数和扰动激波振幅这个未知量时,导出了色散关系.结果表明,正实数γ确是存在.不稳定激波有两种模式,一种模式为γ=-W·k(W<0)它代表激波的绝对不稳定性,是新得到的模式.另一种模式与过去工作中给出的[2,3]大体相同.本文则进一步给出了这种模式的激波不稳定性增长率,并指出j2((?V/?P)_H=1+2M为最不稳定点(即无量纲化的不稳定性增长率Г=∞).如果不假定ω是纯虚数,而是复数,其虚部为正实数Im(ω)≥0.本文也严格证明了其不稳定性判据仍有两种模式,ω仍为纯虚数.     

一维绝热流动中初等波的相互作用

<正> 一维绝热流动的守恒律组(在拉格朗日座标下)为其中u——速度、p——压强、v——比容、E=e+u~2/2,而在多方气体的情形e=pv/(γ-1),绝热指数γ为常数,γ>1.人们称它的某些特解为初等波,其中包括前、后向激波S、S;前、后向中心疏散波R、R和上、下跳接触间断T、T.它们的相互作用一方面在     

一类非线性边值问题解的激波性态

利用激波理论和匹配原理, 在适当的条件下讨论了一类非线性方程的激波问题, 得出了其激波解及其激波位置的表示式.将其结果用于一类可压缩流体流动模型, 较简捷地得到了该模型解的激波性态.     

The singular solutions to a nonsymmetric system of Keyfitz-Kranzer type with initial data of Riemann type

The solutions to the Riemann problem for a nonsymmetric system of Keyfitz-Kranzer type are constructed explicitly when the initial data are located in the quarter phase plane. In particular, some singular hyperbolic waves are discovered when one of the Riemann initial data is located on the boundary of the quarter phase plane, such as the delta shock wave and some composite waves in which the contact discontinuity coincides with the shock wave or the wave back of rarefaction wave. The double Riemann problem for this system with three piecewise constant states is also considered when the delta shock wave is involved. Furthermore, the global solutions to the double Riemann problem are constructed through studying the interaction between the delta shock wave and the other elementary waves by using the method of characteristics. Some interesting nonlinear phenomena are discovered during the process of constructing solutions; for example, a delta shock wave is decomposed into a delta contact discontinuity and a shock wave.     

The Interaction of Shocks with Dispersive Waves II. Incompressible-Integrable Limit

This is the second in a two-part series of articles in which we analyze a system similar in structure to the well-known Zakharov equations from weak plasma turbulence theory, but with a nonlinear conservation equation allowing finite time shock formation. In this article we analyze the incompressible limit in which the shock speed is large compared to the underlying group velocity of the dispersive wave (a situation typically encountered in applications). After presenting some exact solutions of the full system, a multiscale perturbation method is used to resolve several basic wave interactions. The analysis breaks down into two categories: the nonlinear limit and the linear limit, corresponding to the form of the equations when the group velocity to shock speed ratio, denoted by ε, is zero. The former case is an integrable limit in which the model reduces to the cubic nonlinear Schrödinger equation governing the dispersive wave envelope. We focus on the interaction of a “fast” shock wave and a single hump soliton. In the latter case, the ε=0 problem reduces to the linear Schrödinger equation, and the focus is on a fast shock interacting with a dispersive wave whose amplitude is cusped and exponentially decaying. To motivate the time scales and structure of the shock-dispersive wave interactions at lowest orders, we first analyze a simpler system of ordinary differential equations structurally similar to the original system. Then we return to the fully coupled partial differential equations and develop a multiscale asymptotic method to derive the effective leading-order shock equations and the leading-order modulation equations governing the phase and amplitude of the dispersive wave envelope. The leading-order interaction equations admit a fairly complete analysis based on characteristic methods. Conditions are derived in which: (a) the shock passes through the soliton, (b) the shock is completely blocked by the soliton, or (c) the shock reverses direction. In the linear limit, a phenomenon is described in which the dispersive wave induces the formation of a second, transient shock front in the rapidly moving hyperbolic wave. In all cases, we can characterize the long-time dynamics of the shock. The influence of the shock on the dispersive wave is manifested, to leading order, in the generalized frequency of the dispersive wave: the fast-time part of the frequency is the shock wave itself. Hence, the frequency undergoes a sudden jump across the shock layer.In the last section, a sequence of numerical experiments depicting some of the interesting interactions predicted by the analysis is performed on the leading-order shock equations.     

Nonlinear Spatial Evolution of Small Disturbances from Boundary Conditions in Flat Inclined-Channel Flow

The asymptotic behavior of small disturbances as they evolve spatially from boundary conditions in a flat inclined channel is determined. These small disturbances develop into traveling waves called roll waves, first discussed by Dressler in 1949. Roll waves exist if the Froude number F exceeds 2, which consist of a periodic pattern of bores, or discontinuities. After confirming the instability condition for   F > 2  for the linearized equations in the boundary value case, the nonlinear boundary value problem for the weakly unstable region of F slightly larger than 2 is studied. Multiple scales and the Fredholm alternative theorem are applied to determine the evolution of the solution in space. It is found that the solution is dominated by the evolution of the disturbance along one characteristic. The shock conditions governing the asymptotic solution are determined and these conditions are used to determine the approximate shape of the resulting traveling wave from the solution. Both asymptotic and numerical results for periodic disturbances are presented.     

Construction of a series of travelling wave solutions to nonlinear equations

In this paper, based on new auxiliary ordinary differential equation with a sixth-degree nonlinear term, we study the (1 + 1)-dimensional combined KdV–MKdV equation, Hirota equation and (2 + 1)-dimensional Davey–Stewartson equation. Then, a series of new types of travelling wave solutions are obtained which include new bell and kink profile solitary wave solutions, triangular periodic wave solutions and singular solutions. The method used here can be also extended to many other nonlinear partial differential equations.     

内机械激波——海洋激流的一种解释

采用Lagrange坐标和Hamilton原理,推导了二维两层浅水系统的位移法内波方程,并在此基础上研究了二维内机械激波.通过具体的数值算例分析发现内机械激波具有流速大、持续时间短、空间范围狭小、水面存在突变的特点,指出海洋激流就是内机械激波.内机械激波同样也为海洋断崖提供了一种解释.     

On the acceleration of shock waves and concentration of energy

By a series of simple examples related to exact solutions of problems in gas dynamics and magnetohydrodynamics, possible mechanisms of acceleration of shock waves and concentration of energy are elucidated. The acceleration of a shock wave is investigated in the problem of motion of a plane piston at a constant velocity in the case when the initial density of the medium drops in the presence of constant counterpressure. It is shown that in this situation a “blow-up” regime is induced by a shock wave going to infinity in finite time even for limited work of the piston. A simple spherically symmetric solution with a converging shock wave is constructed and shown to lead to the concentration of energy. A general method for solving one-dimensional non-self-similar problems related to matching the equilibrium state to a motion with homogeneous deformation on a shock wave is discussed; this method leads to a solution in quadratures.     

Shock waves for compressible navier-stokes equations are stable

It is shown that shock waves for the compressible Navier-Stokes equations are nonlinearly stable. A perturbation of a shock wave tends to the shock wave, properly translated in phase, as time tends to infinity. Through the consideration of conservation of mass, momentum and energy we obtain an a priori estimate of the amount of translation of the shock wave and the strength of the linear and nonlinear diffusion waves that arise due to the perturbation. Our techniques include the energy method for parabolic-hyperbolic systems, the decomposition of waves, and the energy-characteristic method for viscous conservation laws introduced earlier by the author.     

Stability condition for strong shock waves in the problem of flow around an infinite plane wedge

We consider the thermodynamical equilibrium state flow of an inviscid non-heat-conducting gas flowing around a plane infinite wedge, and study the stationary solution to this problem–the so-called strong shock wave; the flow behind the shock front is subsonic.We find the solution to the linear analog of the original mixed problem, prove that the solution trace on the shock wave is the superposition of the direct and reflected waves, and (the main point) justify the Lyapunov asymptotical stability of the strong shock wave provided that the uniform Lopatinsky condition is fulfilled. The initial data have a compact support, and the solvability conditions occur.     

Interaction of oblique deflagration and shock for two-dimensional steady adiabatic combustion system

The interaction of an oblique deflagration wave and an oblique shock wave for two-dimensional steady adiabatic combustion system is analyzed. Using the shock wave polar and combustion wave polar, we exhibit the construction of the solutions. It is found that the deflagration remains if the shock is weak. However, the shock transforms the deflagration into a detonation(DDT) if it is strong or stops the deflagration if it is proper.