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三维弹性固体中冲击波传输方程的Lagrange描述 总被引:1,自引:1,他引:0
在Lagrange坐标中导出了三维非线性弹性固体中冲击波幅度在任意传播方向上的传输方程.导出的方程说明,冲击波的幅度在任意传播方向上随时间的变化率依赖于(i)冲击波阵面紧后方介质运动的一个未知量;(ii)冲击波阵面的两个主曲率;(iii)冲击波法向波速在阵面内的表面梯度;(iv)和冲击波前方介质运动有关的非齐次项,当前方介质处于均匀运动状态时此项为零.文中指出了适当选择传播矢量以简化传输方程的几种方法.我们还得到了一组与介质本构方程无关的、联系冲击波各跳跃量变化率的普适关系. 相似文献
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对螺旋型旋风分离器进行了两相流场的三维数值模拟.气体流场通过求解三维N-S方程得到,湍流模型采用了雷诺应力模型.计算结果表明,旋风分离器内部的流场分为两部分:螺旋通道内比较稳定的流场和简体中心区域的复合涡结构流场.对颗粒运动轨迹的计算表明,颗粒在入口处的初始位置对颗粒分离有比较显著的影响.同时得到了不同入口速度下颗粒的分级效率曲线,并给出了气体流量对旋风分离器性能的影响,结果显示:气体流量的增加会提高分离效率.但同时导致压力损失的急剧增加. 相似文献
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单位球面的三维紧致极小子流形 总被引:3,自引:0,他引:3
本文得到高维球面上三维紧致极小子流形的若干刚性定理.在一个整体拚挤条件下,数量曲率的拚挤常数被改进了,也对李奇曲率的拚挤问题进行了讨论. 相似文献
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本文首先利用几何奇异摄动方法,证明了粘性系数充分小时一类非凸粘性平衡律方程的粘性冲击波的存在性,推广了原来在非线性项严格凸的条件下得到的结果.进而,利用谱分析和上下解方法,证明了对固定的小的粘性系数此类波是全局渐近指数稳定的,推广了反应扩散方程中经典的全局稳定性结果. 相似文献
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关于判断三维欧氏空间中的一张曲面是否为凸曲面之问题,以前曾经有过一些讨论,给出了一些判别条件.但是那些判别条件都是以几何图形的关系来表述,因此不便于计算.我们现在试图找出一个判别条件,能以方程之间的关系来表述以便能有助于计算,我们这里对于凸曲面的定义以及一些有关的概念参见. 我们先对平面曲线来证明以下的 相似文献
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In this paper the kinematics of a curved shock of arbitrary strength has been discussed using the theory of generalised functions.
This is the extension of Moslov’s work where he has considered isentropic flow even across the shock. The condition for a
nontrivial jump in the flow variables gives the shock manifold equation (sme). An equation for the rate of change of shock
strength along the shock rays (defined as the characteristics of the sme) has been obtained. This exact result is then compared
with the approximate result of shock dynamics derived by Whitham. The comparison shows that the approximate equations of shock
dynamics deviate considerably from the exact equations derived here. In the last section we have derived the conservation
form of our shock dynamic equations. These conservation forms would be very useful in numerical computations as it would allow
us to derive difference schemes for which it would not be necessary to fit the shock-shock explicitly. 相似文献
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Peter Howard 《偏微分方程通讯》2013,38(1):73-121
ABSTRACT We consider degenerate viscous shock waves arising in systems of two conservation laws, where degeneracy describes viscous shock waves for which the asymptotic endstates are sonic to the hyperbolic system (the shock speed is equal to one of the characteristic speeds). In particular, we develop detailed pointwise estimates on the Green's function associated with the linearized perturbation equation, sufficient for establishing that spectral stability implies nonlinear stability. The analysis of degenerate viscous shock waves involves several new features, such as algebraic (nonintegrable) convection coefficients, loss of analyticity of the Evans function at the leading eigenvalue, and asymptotic time decay of perturbations intermediate between that of the Lax case and that of the undercompressive case. 相似文献
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In this paper we give a theoretical foundation to the asymptotical development proposed by V. P. Maslov for shock type singular solutions of conservations laws, in the framework of Colombeau theory of generalized functions. Indeed, operating with Colombeau differential algebra of simplified generalized functions, we proof that Hugoniot–Maslov chains are necessary conditions for the existence of shock waves in conservation laws with polynomial flows. As a particular case, these equations include the Hugoniot–Maslov chains for shock waves in the Hopf equation. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Angelo Morro 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1978,29(5):822-827
Summary Transmission and reflexion of plane acoustic waves through a longitudinal shock wave in elastic isotropic solids are investigated. As a result, the amplitude of the transmitted and reflected waves and the jump of the acceleration of the shock are explicitly determined.
Résumé On envisage la transmission et la réflexion d'une onde acoustique plane par une onde de choc longitudinale dans les solides élastiques isotropes. On détermine explicitement l'amplitude des ondes transmises et réflechies et le saut de l'acceleration du choc.相似文献
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Corrado Lattanzio Denis Serre 《NoDEA : Nonlinear Differential Equations and Applications》1999,6(3):319-340
We consider the interaction between shock waves in a semilinear relaxation approximation to N×N systems of conservation laws. This interaction is described by proving the existence of a particular solution to the relaxing
system, with a certain asymptotic as
Received July 1998 相似文献
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本文研究了磁气体动力学守恒律方程组的基本波,给出了基本波曲线的表达式,并利用所得到的表达式证明了基本波曲线的一些性质. 相似文献
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This paper studies the combination of rarefaction wave and shock wave for the hyperbolic conservation laws and establishes the local existence of such combination of waves in the multi-dimensional space. 相似文献
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The paper solves analytically the Riemann problem for a nonstrictly hyperbolic system of conservation laws arising in geometrical optics,in which the flux contains the nonconvex function possessing an infinite number of inflection points.Firstly,the generalized Rankine–Hugoniot relations and entropy condition of delta shock waves and left(right)-contact delta shock waves are proposed and clarified.Secondly,with the help of the convex hull,seven kinds of structures of Riemann solutions are obtained.The solutions fall into three broad categories with a series of geometric structures involving simultaneously contact discontinuities,vacuums and delta shock waves.Finally,numerical experiments confirm the theoretical analysis. 相似文献