静脉血流动力学模型基本波的相互作用北大核心CSCD

静脉系统是心血管系统的重要组成部分.脉搏波在血液流动中有着突出的重要性.本文主要研究静脉血流动力学模型基本波的相互作用.血流动力学模型是2×2严格双曲型方程组,其基本波包括疏散波和激波,属于血液流动中的脉搏波.基本波相互作用后血管截面面积和血流速度发生相应的变化.     

血液动力学中血管流激波与驻波的相互作用

血液动力学问题是生物力学心血管系统中的重要研究课题.血管内斑块处,血管截面和血管壁的材质发生变化,对血液流动产生重要影响.血液流动中基本波及其相互作用对探究血液流动的规律、生理学意义及与疾病的关系有着重要的意义.本文研究血液动力学血液流动简化数学模型的基本波的相互作用.血管流模型是3×3非严格双曲型方程组.构造性地得到了初值为三段常状态时,血管流问题的解,即解决了激波与驻波的相互作用问题.特别地,给出四种后前激波与驻波的相互作用的结果.     

The Riemann Problem for Chaplygin Gas Flow in a Duct with Discontinuous Cross-Section

The fluid flows in a variable cross-section duct are nonconservative because of the source term. Recently, the Riemann problem and the interactions of the elementary waves for the compressible isentropic gas in a variable cross-section duct were studied. In this paper, the Riemann problem for Chaplygin gas flow in a duct with discontinuous cross-section is studied. The elementary waves include rarefaction waves, shock waves, delta waves and stationary waves.     

二维拟定常可压流Euler方程组的简单波

简单波是这样的流动,它在像空间中的像是一条曲线．“简单波理论是除基本流动结构以外构造流动问题的解的基础”,见Courant和Friedrichs的经典著作《超声速流与冲击波》．该文主要研究二维拟定常可压流Euler方程组的简单波的几何结构.根据这些几何诠释,还构造了绕一拟流线弯曲部的疏散和压缩的简单波流动结构．这种流动结构将作为一个局部流动结构出现在4个接触间断的Riemann问题的整体解中．     

Solutions to a hyperbolic system of conservation laws on two boundaries

This paper studies the interaction of elementary waves including delta-shock waves on two boundaries for a hyperbolic system of conservation laws. The solutions of the initialboundary value problem for the system are constructively obtained. In the problem the initialboundary data are in piecewise constant states.     

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.     

有限深度两层流体系统中运动点源生成的内波及其与自由面的相互作用

基于水波动力学势流理论,以二流体系统中点源运动为基本模型,采用Green函数法,研究了分层流体中内部扰动诱生的内波对自由面的影响,探讨对合成孔径雷达成像起重要作用的自由面辐散场的变化规律。研究表明:当上下层流体密度跃变较大、源接近密跃层且Froude数Fr接近内波模式的临界值Fr₂时,内波模式导致的自由面辐散场强度与表面波模式的贡献相当,两者具有强烈的耦合作用,理论分析与实验结果定性一致。     

二维零压气体动力学系统的黎曼问题-3J情形

研究二维零压气体动力学系统带有三片常数的黎曼问题.对外波为3J的情形,借助特征分析方法,通过研究基本波的相互作用,构造了两种不同的显式解结构,一种出现了δ-激波,另一种则包含一个三角形真空区域.     

相变演化Suliciu模型中波的相互作用

描述相变演化的Suliciu模型，其基本波可由行波分析得到．对于任何给定分两段常值的初始状态，相应的Riemann解是某些基本波的组合．对分三段常值的初始状态，解由上述Piemann解构成，其中相邻两状态间以基本波连接．当基本波发生碰撞时，新的Riemann问题形成．通过研究这些Riemann。问题，可以在适当的参数空间中对基本波之间复杂的相互作用加以分类．     

Interaction of elementary waves on a boundary for a hyperbolic system of conservation laws

In this paper, we study the interaction of elementary waves including delta‐shock waves on a boundary for a hyperbolic system of conservation laws. A boundary entropy condition is derived, thanks to the results of Dubois and Le Floch (J. Differ. Equations 1988; 71 :93–122) by taking a suitable entropy–flux pair. We obtain the solutions of the initial‐boundary value problem for the system constructively, in which initial‐boundary data are piecewise constant states. Copyright © 2008 John Wiley & Sons, Ltd.     

Global existence of shock front solution to axially symmetric piston problem in compressible flow

In this paper we study the global existence of BV solution to two-dimensional piston problem in fluid dynamics. Different from previous results on related problems we remove the restriction on the strength of the leading shock and require the velocity of the piston is rather fast or the density is quite small instead. The main tool in our proof is Glimm Scheme with some improvement. To define the Glimm functional we derive more precise estimates for the interaction of elementary waves, particularly in the region near the leading shock. The paper is partially supported by National Natural Science Foundation of China 10531020, the National Basic Research Program of China 2006CB805902 and the Doctorial Foundation of National Educational Ministry 20050246001.     

Stability of a superposition of shock waves with contact discontinuities for systems of viscous conservation laws

In this paper, we show the large time asymptotic nonlinear stability of a superposition of viscous shock waves with viscous contact waves for systems of viscous conservation laws with small initial perturbations, provided that the strengths of these viscous waves are small with the same order. The results are obtained by elementary weighted energy estimates based on the underlying wave structure and a new estimate on the heat equation.     

The Riemann problem for an isentropic ideal dusty gas flow with a magnetic field

This paper deals with Riemann problem for one-dimensional inviscid, isentropic, and perfectly conducting ideal dusty gas flow with a transverse magnetic field. The explicit expressions of elementary waves are derived in terms of the density, velocity, and transverse magnetic induction of an ideal dusty gas flow. The analytical properties of elementary wave curves and the influence of parameter on the elementary waves are discussed. A new approach is proposed to resolve the Riemann problem. By applying this approach, we obtain 10 kinds of exact solutions and their corresponding criteria.     

自由表面与粘性尾迹的相互作用

解析地研究了无限深不可压粘性流体中运动物体产生层流尾迹与自由表面波的相互作用．以定常的Oseen方程模拟受扰流动,对于小振幅自由表面波则采用线性化的运动学和动力学边界条件．在数学描述上,运动物体以Oseen极子模拟,受扰流场分解成表述粘性尾迹的无界奇异Oseen流和描述自由面效应的有界正则Oseen流之和．通过积分变换法,得到自由表面波的精确解．借助Lighthill的两步格式,导出了自由面波高带有附加校正项的渐近解．所得对称解显示了波动的振幅因粘性和潜深的存在而呈指数衰减．     

一维Chaplygin气体欧拉方程组中波的相互作用

研究一维Chaplygin气体欧拉方程组中波的相互作用.方程组的波包含接触间断和在密度变量以及内能变量上同时具有狄拉克函数的狄拉克激波.根据这些波的不同组合,问题被分成了7种情形.通过详细地构造每种情形的整体解,获得了各种波相互作用的完整结果.特别地,对于一类初值,两个接触间断相互作用后,产生了一个狄拉克激波;然而,对于另外一类初值,一个狄拉克激波与一个接触间断相互作用后,狄拉克激波消失.这些都是波相互作用中非常特别的现象.     

一类二维单个守恒律方程的Riemann问题

本文研究一类二维单个守恒律方程的Riemann问题.用广义特征分析方法研究了这类方程,给出了基本波的分类,解决了初值为两片常数的二维Riemann问题,给出了Riemann解.     

Exact Free Surface Flows for Shallow Water Equations I: The Incompressible Case

A comprehensive exact treatment of free surface flows governed by shallow water equations (in sigma variables) is given. Several new families of exact solutions of the governing PDEs are found and are shown to embed the well-known self-similar or traveling wave solutions which themselves are governed by reduced ODEs. The classes of solutions found here are explicit in contrast to those found earlier in an implicit form. The height of the free surface for each family of solutions is found explicitly. For the traveling or simple wave, the free surface is governed by a nonlinear wave equation, but is arbitrary otherwise. For other types of solutions, the height of the free surface is constant either on lines of constant acceleration or on lines of constant speed; in another case, the free surface is a horizontal plane while the flow underneath is a sine wave. The existence of simple waves on shear flows is analytically proved. The interaction of large amplitude progressive waves with shear flow is also studied.     

Effect of nonlinear wave-current interaction on flow fields and hydrodynamic forces

A fifth-order theory for solving the problem of interaction between Stokes waves and exponential profile currents is proposed. The calculated flow fields are compared with measurements. Then the errors caused by the linear superposition method and approximate theory are discussed. It is found that the total wavccurrent field consists of pure wave, pure current and interaction components. The shear current not only directly changes the flow field, but also indirectly does so by changing the wave parameters due to wave-current interaction. The present theory can predict the wave kinematics on shear currents satisfactorily. The linear superposition method may give rise to more than 40% loading error in extreme conditions. When the apparent wave period is used and the Wheeler stretching method is adopted to extrapolate the current, application of the approximate theory is the best. Project supported by the Chinese Academy of Sciences.     

A NOTE ON THE INTERACTIONS OF ELEMENTARY WAVES FOR THE AR TRAFFIC FLOW MODEL WITHOUT VACUUM

In this note, we consider the interactions of elementary waves for the traffic flow model proposed by Aw and Rascle when the vacuum is not involved. The solutions are obtained constructively and globally when the initial data consist of three pieces of constant states. Furthermore, it can be found that the Riemann solutions are stable with respect to such small perturbations of the initial data in this particular situation by investigating the limits of the solutions as the perturbed parameter ε goes to zero.     

Interaction of Shallow Water Waves

In this paper, we consider the Riemann problem and interaction of elementary waves for a nonlinear hyperbolic system of conservation laws that arises in shallow water theory. This class of equations includes as a special case the equations of classical shallow water equations. We study the bore and dilatation waves and their properties, and show the existence and uniqueness of the solution to the Riemann problem. Towards the end, we discuss numerical results for different initial data along with all possible interactions of elementary waves. It is noticed that in contrast to the p -system, the Riemann problem is solvable for arbitrary initial data, and its solution does not contain vacuum state.