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 .     

运动气流的二维激波动力学方程组

本文把原来适用于波前为静止气体的激波动力学方法,推广到波前为运动气流的情况中。导出了以激波马赫数和波面方向角表示的波前为均匀流的二维激波动力学方程组和波前为非均匀流的二维激波动力学方程组。文中还简单介绍了运动气流的激波动力学方程组在“双波干扰”中的应用。     

二维超音速混合层中小激波的存在及其对流场结构的影响

在二维超音速混合层入口处引入T-S波及其亚谐波,对扰动的空间演化进行了数值模拟.研究了由扰动引发的小激波(shocklet)的强度与入口处扰动幅值的关系.分析了激波前后扰动速度剖面的变化,发现小激波的存在对扰动速度剖面有显著影响,而高速层和低速层中激波对扰动速度作用不同.     

不可压缩弹性固体中的二维应力波分析

本文研究不可压缩弹性固体中的二维应力波.首先对一般的应变能函数给出了分析简单波和激波的基本方程,然后求出了波速和相应的本征向量,证明在一般情况下有两组简单波和两组激波,最后举了平面变形和反平面变形两个例子.在平面变形的情况下,平面激波的斜反射问题一般无解.     

激波在变截面管道中的传播及新激波的产生与发展

由于爆炸或各种不同的原因在介质中引起的压缩作用,如以超声速传播就形成激波。当一个强激波进入变截面管道后,由于管道截面积的变化,激波强度也发生变化,其后面形成不定常气流。为了探讨激波及其后面的不定常气流的变化规律,我们用三种方法进行数值计算,即:一维特征线法,一维两步二阶差分法及轴对称二维两步二阶差分法。计算结果,三种方法相辅相成,并弄清了管内的流场。计算表明,第一个激波过后在连续流中很快出现了新的激波,并逐渐增强。二维不定常方法还算出了三叉波的形成。     

基于第二粘性用局部微分求积法计算激波

考虑第二粘性效应,采用局部微分求积法数值求解激波问题．首先解释了在激波计算时,有必要考虑第二粘性,然后基于粘性模型,对一维和二维激波进行了数值模拟,还分别考察了剪切粘性力和第二粘性力对数值结果的影响．结果表明,采用粘性模型加上局部微分求积法能够模拟出激波特征,具有客观、简单的优点．     

基于非结构自适应网格的复合有限体积法

利用文献[1]中将Lax-Wendroff格式和Lax-Friedrichs格式整体复合作用构成二维无结构网格上的复合型有限体积法,同时利用Delaunay方法,根据流场流动特性变化的梯度值为指示器对网格进行加密和粗化,实现自适应,并将此方法应用到二维浅水波方程的求解上,进行了二维部分溃坝,倾斜水跃的数值实验.结果表明,该方法是一个计算稳定、能适应复杂的求解域、能很好地捕捉激波、且计算速度快的算法.     

关于海洋动力学中二维的大尺度原始方程组(Ⅰ)

考虑地球物理学中大尺度海洋运动的二维原始方程组的初边值问题．先假定海洋的深度为正的常数．首先,当初始数据是平方可积时,应用Faedo-Galerkin方法,得到了这一问题整体弱解的存在性．其次,当初始数据及其它们关于垂直方向的导数均为平方可积时,应用Faedo-Galerkin方法和各向异性不等式,得到了上述初边值问题的整体弱强解的存在、唯一性．     

非齐次二维Burgers方程的非自相似黎曼解的奇性结构

该文研究了二维非齐次Burgers方程Riemann问题的激波解和稀疏波解之间相互作用的全局奇性结构及其演化,其中初值被两个相离的圆隔开并分成三片常数.首先得到了由初值间断发出的激波解和稀疏波解的表达式;其次,讨论了这些激波和稀疏波的相互作用,并发现了一些新现象,其与齐次情形相比,激波和稀疏波能一直相互作用,相互作用的时间没有使得结构发生改变的临界值;最后构造了非自相似解的全局结构,并发现了有别于齐次情形的渐近行为,即基本波区域的直径是有界的.     

基于AUSM分裂的二维通量分裂格式

基于对流迎风分裂思想构造的AUSM类格式具有简单、高效、分辨率高等优点,在计算流体力学中得到了广泛的应用.传统的AUSM类格式在计算界面数值通量时只考虑网格界面法向的波系,忽略了网格界面横向波系的影响.使用Liou-Steffen通量分裂方法将二维Euler方程的通量分裂成对流通量和压力通量,采用AUSM格式来分别计算对流数值通量和压力数值通量.通过求解考虑了横向波系影响的角点数值通量来构造一种真正二维的AUSM通量分裂格式.在计算一维算例时,该格式保留了精确捕捉激波和接触间断的优点.在计算二维算例时,该格式不仅具有更高的分辨率而且表现出更好的鲁棒性,可以消除强激波波后的不稳定现象.此外,在多维问题的数值模拟中,该格式大大地提高了稳定性CFL数,具有更高的计算效率.因此,它是一种精确、高效并且强鲁棒性的数值方法.     

研究金属中激波构造与衰减的一个物理模型

本文给出了研究金属中激波构造与衰减的一个物理模型.为了建立高速形变下材料的本构方程和研究激波过渡带的构造,需要考虑二个独立的理论方面.首先,将比内能分解成弹性压缩能和弹性形变能,而将形变能作为弹性应变和熵的函数展开到三阶项,其中考虑了热与机械能的耦合效应.其次,从位错动力学角度建议了一个塑性松弛函数以便描述高温、高压下塑性流动的特性.另外,本文给出了一个常微分方程组用以计算定态激波过渡带中各状态变量的分布以及激波的厚度.倘若假定在激波上熵的跳跃可以忽略,并用Hugoniot压缩模量代替等熵压缩摸量,可以获得一个分析解.最后,本文还提出了求解平板对称碰撞中激波波头衰减的一个近似方法。     

The Evolution of Internal Undular Bores over a Slope in the Presence of Rotation

The large‐amplitude internal waves commonly observed in the coastal ocean often take the form of unsteady undular bores. Hence, here, we examine the long‐time combined effect of variable topography and background rotation on the propagation of internal undular bores, using the framework of a variable‐coefficient Ostrovsky equation. Because the leading waves in an internal undular bore are close to solitary waves, we first examine the evolution of a single solitary wave. Then, we consider an internal undular bore, for which two methods of generation are used. One method is the matured undular bore developed from an initial shock box in the Korteweg–de Vries equation, that is the Ostrovsky equation with the rotational term omitted, and the other method is a modulated cnoidal wave solution of the same Korteweg–de Vries equation. It transpires that in the long‐time model simulations, the rotational effect disintegrates the nonlinear waves into inertia‐gravity waves, and then there emerge complicated interactions between these inertia‐gravity waves and the modulated periodic waves of the undular bore, especially at the rear part of the undular bore. However, near the front of the undular bore, nonlinear effects further modulate these waves, with the eventual emergence of nonlinear envelope wave packets.     

Burgers方程的激波解与激波位置(英文)

讨论了Burgers方程激波解和位置的转移 .认为 :对该类方程 ,当边值发生微小变化时 ,不仅激波解发生变化 ,而且激波位置将发生较大的变化 ,甚至从内层移到边界 .其激波解也会发生相应的变化 .     

Two layer transient water waves over a viscoelastic ocean bed

A two-layer analysis of the transient development of water waves over a viscoelastic ocean bed is presented here. This is a two-dimensional initial value investigation of the transient development of surface and internal wave motions governed by harmonic pressure distribution acting on the free surface in an inviscid liquid over a viscous and elastic ocean bed. The equations of motion and the equation of continuity are described in terms of velocity potential and stream functions. The solution of this problem is obtained by using Laplace and Fourier transform methods. Limiting case of the layers to obtain free surface elevation is also presented.     

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.     

An integro-differential equation for surface ocean waves with finite depth

An explicit integro-differential equation formulation is derived for surface ocean waves with finite depth. The equation involves only 2D surface variables. For this equation, we establish the stability and existence of solutions, and explain the effect of depth on surface wave properties.     

Shock Formation for 2D Isentropic Euler Equations with Self-similar Variables

The author studies the 2D isentropic Euler equations with the ideal gas law. He exhibits a set of smooth initial data that give rise to shock formation at a single point near the planar symmetry. These solutions to the 2D isentropic Euler equations are associated with non-zero vorticity at the shock and have uniform-in-time 1 3-H¨older bound. Moreover, these point shocks are of self-similar type and share the same profile, which is a solution to the 2D self-similar Burgers equation. The proof of the solutions, following the 3D construction of Buckmaster, Shkoller and Vicol (in 2023), is based on the stable 2D self-similar Burgers profile and the modulation method.     

Global Conic Shock Wave for the Steady Supersonic Flow Past a Large Curved Cone at Infinity

In this paper, we establish the global existence and stability of a steady symmetric shock wave for the constant supersonic flow past an infinitely long and large curved conic body. The flow is assumed to be polytropic, isentropic and described by a steady potential equation. Through looking for the suitable “dissipative” boundary conditions on the shock and the conic surface together with the special form of shock equation, we show that the conic shock attached at the vertex of the cone exists globally in the whole space when the speed of the supersonic incoming flow is appropriately large.     

Surface waves due to blasts on and above inviscid liquids of finite depth

For the problem of waves due to an explosion above the surface of a homogeneous ocean of finite depth, asymptotic expressions of the velocity potential and the surface displacement are determined for large times and distances from the pressure area produced by the incident shock. It is shown that the first item in Sakurai's approximation scheme for the pressure field inside the, blast wave as well as the results of Taylor's point blast theory can be used to yield realistic expressions of surface displacement. Some interesting features of the wave motion in general are described. Finally some numerical calculations for the surface elevation were performed and included as a particular case.     

An Interaction of a Rarefaction Wave and a Transonic Shock for the Self-Similar Two-Dimensional Nonlinear Wave System

We study a two dimensional Riemann problem for the self-similar nonlinear wave system which gives rise to an interaction of a transonic shock and a rarefaction wave. The interesting feature of this problem is that the governing equation changes its type from supersonic in the far field to subsonic near the origin. The subsonic region is then bounded above by the sonic line (degenerate) and below by the transonic shock (free boundary). Furthermore due to the rarefaction wave in the downstream, which interacts with the transonic shock, the problem becomes inhomogeneous and degenerate. We establish the existence result of the global solution to this configuration, and present analysis to understand the solution structure of this problem.