一类非线性奇摄动方程的激波问题

利用奇摄动理论和匹配原理，讨论了一类非线性奇摄动方程的激波问题．首先，构造了原问题的外部解和内层解．其次，研究了当激波在区间的边界附近和内部的激波解．最后，得出了与边界条件相对应的激波位置及解的表达式．     

一类奇摄动非线性方程的激波解

利用匹配条件讨论一类奇摄动非线性方程激波解．得出了对应的激波解与边界条件的关系．     

非线性退化波方程的Riemann问题

研究了弹性力学中一退化波方程的Riemann问题．其应力函数非凸非凹,从而使得激波条件退化．通过引入广义激波条件下的退化激波,构造性地得到了各种情形下Riemann问题的整体解．     

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 .     

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.     

用Lebesgue－Stieltjes积分定义的双曲型方程广义解

该文用Ｌｅｂｅｓｇｕｅ－Ｓｔｉｅｌｔｊｅｓ积分给出一个双曲型方程组广义解的新定义，在这个意义下证明了Ｃａｕｃｈｙ问题整体广义解的存在性．这种解自然地包含了δ－激波．     

弱斜激波的稳定性

讨论平面斜激波对固壁扰动的稳定性. 通过对沿光滑固壁的定常超音速流的激波生成、激波整体构造以及解的渐近性态的分析, 得到了含弱平面斜激波的广义解的稳定性,它可以作为熵条件的补充用于选取物理上合理的广义解.     

一类非线性方程的激波解

该文是利用匹配条件讨论一类非线性方程激波解。得出了对应的激波解与边界条件的关系。     

延拓Chaplygin气体黎曼解的流逼近极限过程中的集中性研究(英文)

本文研究了延拓Chaplygin气体的黎曼解在流逼近极限过程中的集中现象和狄拉克激波的两种形成机制问题.利用相平面分析法和广义特征分析法,构造出了延拓Chaplygin气体的整体黎曼解,并获得了两个结果:当压力消失时,延拓Chaplygin气体的包含两个激波的解收敛到输运方程的狄拉克激波解;当压力项趋近于广义Chaplygin压力项时,延拓Chaplygin气体的包含两个激波的解收敛到广义Chaplygin气体的狄拉克激波解.结论推广到了延拓Chaplygin气体.     

p方程组的激波生成与构造

讨论p-方程组的激波生成与构造.精细地刻画了从光滑解到激波产生的转变过程,并给出了在激波生成点附近奇性结构与解的估计.     

一类奇摄动非线性边值问题激波解的Sinc-Galerkin方法

讨论了一类非线性奇摄动方程的激波问题.利用Sinc-Galerkin方法,构造出边值问题的激波解,并由Newton法得到其近似解.     

计算激波的高精度数值方法

在分析了数值解在激波附近产生非物理振荡的原因后,构造了一个三阶迎风紧致格式以及激波的捕捉技术,并且,提出一种称为准装配法的新的激波装配方法.一维流动的数值试验表明,新方法是非常令人满意的.     

Least‐squares finite element method on adaptive grid for PDEs with shocks

We apply the least‐squares finite element method with adaptive grid to nonlinear time‐dependent PDEs with shocks. The least‐squares finite element method is also used in applying the deformation method to generate the adaptive moving grids. The effectiveness of this method is demonstrated by solving a Burgers' equation with shocks. Computational results on uniform grids and adaptive grids are compared for the purpose of evaluation. The results show that the adaptive grids can capture the shock more sharply with significantly less computational time. For moving shock, the adaptive grid moves correctly with the shock. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

基于GARCH方法研究非效率投资中金融冲击的影响机理

代理理论认为,在动荡和不确定环境下,管理者会做出偏离企业价值最大化的非效率投资行为。为探究金融冲击这个带有不确定色彩的因素,是否会恶化企业非效率投资行为,论文先是使用一个数学模型来说明金融冲击与非效率投资的可能关系,而后以GARCH方法的条件异方差来度量金融冲击的潜变量股市冲击、货币冲击和汇率冲击。最后,实证检验了这三个金融冲击潜变量和非效率投资的关系。研究发现:货币冲击和汇率冲击会显著提升非效率投资,而股市冲击能够显著降低非效率投资。进一步研究表明,货币冲击和汇率冲击会通过显著增加过度投资来加大非效率投资行为,而股市冲击则通过显著减少投资不足来达到降低非效率投资行为。     

Dynamically adapted grids for interacting discontinuous solutions

Further development of the dynamic adaptation method for gas dynamics problems that describe multiple interactions of shock waves, rarefaction waves, and contact discontinuities is considered. Using the Woodward-Colella problem and a nonuniformly accelerating piston as examples, the efficiency of the proposed method is demonstrated for the gas dynamics problems with shock wave and contact discontinuity tracking. The grid points are distributed under the control of the diffusion approximation. The choice of the diffusion coefficient for obtaining both quasi-uniform and strongly nonuniform grids for each subdomain of the solution is validated. The interaction between discontinuities is resolved using the Riemann problem for an arbitrary discontinuity. Application of the dynamic adaptation method to the Woodward-Colella problem made it possible to obtain a solution on a grid consisting of 420 cells that is almost identical to the solution obtained using the WENO5m method on a grid consisting of 12 800 cells. In the problem for a nonuniformly accelerating piston, a proper choice of the diffusion coefficient in the transformation functions makes it possible to generate strongly nonuniform grids, which are used to simulate the interaction of a series of shock waves using shock wave and contact discontinuity tracking.     

He's homotopy perturbation method for solving the shock wave equation

In this article, we discuss the analytic solution of the fully developed shock waves. The homotopy perturbation method is used to solve the shock wave equation, which describes the flow of gases. Unlike the various numerical techniques, which are usually valid for short period of time, the solution of the presented equation is analytic for 0 < t < ∞. The results presented converge very rapidly, indicating that the method is reliable and accurate.     

Thermal Shock Crack Propagation of Alumina Simulated With the Phase-Field Method Under Temperature-Dependent Damage Criteria北大核心CSCD

氧化铝陶瓷材料的力学性能受温度影响显著,因此使用相场法模拟热冲击裂纹的扩展时有必要考虑损伤判据的温度相关性.在现有热力学相场模型的基础上通过引入温度相关性损伤判据,修正了相场模型的控制方程.利用该模型对氧化铝陶瓷热冲击实验进行有限元模拟,并将模拟结果与氧化铝热冲击实验结果和不考虑温度相关性损伤判据的有限元模拟结果进行对比.结果表明,通过引入温度相关性损伤判据,可实现对热冲击裂纹的萌生和扩展过程更合理的模拟.     

An inverse problem for supersonic flow past a curved wedge

This paper studies an inverse problem for supersonic potential flow past a curved wedge, in which we design a suitable curved wedge such that the shock produced by the curved wedge can be controlled to the given position. Under suitable conditions, by characteristic method, we prove the existence of the global classical solution to this inverse problem and develop an optimal decay rate on the given shock’s second order derivatives. We finally construct a specific wedge such that the shock generated by the wedge is a convex combined one.     

COMPUTATION OF NONEQUILIBRIUM HYPERSONIC FLOW OVER CONCAVE CORNERS

1. IntroductionWe consider steady inviscid hyPersonic flow of air about a concave corner including chendcalreaction effects. Computation of nonequllibrium flow is duncult because of the steep gradielltsbehind the shock and an entroPy layer near the body For many cases the time scale of theChemical reactions is 1arger than, or close to, the time scale of the origina1 meChanical problemand the equllibrium chendstry mode1 is not realistic. Therefore, it is necessary to eva1uate thekinetics of c…     

Smooth volume integral conservation law and method for problems in Lagrangian coordinates

An integral conservation law is derived for smooth volume in Lagrangian coordinates (a comoving frame). A method for approximation of the integral smooth volume conservation law is discussed. An extension technique is suggested for development of smooth volume schemes. For hyperbolic systems, smooth volume upwind and Godunov schemes with monotonic reconstruction are derived. The schemes are applied to equations of gas dynamics and tested for three gas-dynamics shock tube problems. The solutions are monotonic and precise. This article was submitted by the author in English.