各向异性弹性体光滑接触界面上的滑移脉冲波

利用Stroh公式,Fourier分析和奇异积分方程技术研究了两各向异性弹性半空间光滑接触可分离界面上滑移脉冲波的存在及其传播特性。结果表明,如果至少能在一种介质中存在Rayleigh波,且其波速小于两种介质中的最小极限速度,则滑移脉冲波就可以存在。这种脉冲波传播速度不确定,可在最小极限波速与较低的Rayleigh波速之间取值,而该取值范围又取决于无界面分离情况下的第一、第二滑移波的解。分离区大小取决于扰动的强度,界面法向力和质点速度在分离区两端有 1 /2奇异性。     

在动网格上的多介质界面数值处理方法研究

运用动网格上的ALE方法对一维可压缩多介质Riemann问题进行求解，在处理介质界面 上的数值通量时提出了3种不同的数值方法：Lagrange方法、GFM和HLLC方法，并且对 这3种方法的数值结果进行了比较，认为GFM方法和HLLC方法在介质界面上出现大压力 梯度时能够明显消除界面上密度的非物理震荡，提高介质界面上数值解的精度.     

一种考虑虚拟质量力的两相压力波速经验模型

前人建立的两相压力波速经验模型未考虑虚拟质量力,本文考虑虚拟质量力、管壁弹性、管壁粗糙度等因素,通过求解双流体模型的小扰动,提出了一种新的气液两相压力波速经验模型．以一个具体的工程实例为背景,运用数值方法对其求解,得到的计算结果与前人实测的实验数据一致．结果表明,当空隙率较小时(0＜Φ＜15%)时,虚拟质量力对压力波速的影响不大,当空隙率较大时(Φ≥15%),考虑虚拟质量力计算的压力波速远大于不考虑虚拟质量力计算的压力波速．经验公式也可达到准确求解压力波速的目的．     

关於动脉中的脉动流

本文根据人体动脉中血液流动的基本特征,首先对描述血液运动的Navier-Stokes方程和描述管壁运动的Lamb方程进行量级估计,并依照Womersley数α以及动脉管的壁厚h与直径d之比的大小,将人体动脉归结为四种不同的模型。本文推得了不同的模型各自对应的基本方程组,并借助于这些方程组导得脉搏波波速的表达式。除了得到一些经典的波速结果之外,本文还得到了一些新的波速表述式。     

动力松弛方法中Rayleigh阻尼参数取值分析

论文阐述了动力松弛法计算静力问题的原理,分析了Rayleigh阻尼对计算的影响,提出了一种对质量阻尼和刚度阻尼参数取值的新方法。这种取值方法可以避免计算结果的振荡和过塑性的问题,并利用实例计算进行了对比分析,验证了本文中Rayleigh阻尼取值的合理性。     

近海结构动力学Ⅱ.随机平均分析

1.引言近10年来,人们大有兴趣的是近海空间桁架型结构在随机波作用下的动力响应预测。一般用修改后可以计及结构运动的著名的Morison方程来计算波浪力。就象在本文第Ⅰ部分中所讨论过的那样,假如采用这个方程,则波-结构系统是非线性的。即使忽略激励对响应的非线性关系(在阻力项中,响应起因于相对波速,而不是绝对波速),所得到的与非线性结构系统有关的力函数中仍包含着质点运动学量的非线性变换。这隐含着在一个高斯波场中,波力并不具有高斯概率密度。如果假定响应速度与波质点速度相比是很小,但不能      

一种鲁棒的HLLC格式及其稳定性分析

精确捕捉接触波和剪切波的Godunov型数值方法，如流行的HLLC格式，在模拟高超声速流动问题时会出现激波异常现象。对HLLC格式进行稳定性分析发现，流体主流方向的扰动都能有效衰减，但是横向的密度与剪切速度的扰动不会衰减。具有特殊对称性的二维Sedov爆轰波问题证明了横向通量和不稳定现象之间的密切联系。利用压力比和马赫数来探测数值激波层亚声速区的横向网格界面，并且在该界面的数值通量上增加熵波粘性和剪切波粘性来构造一种激波稳定的HLLC格式。分析表明，在熵波粘性和剪切波粘性的作用下，横向的所有扰动都会衰减。一系列数值测试证明了新格式不仅可以成功地抑制各类激波异常现象，还保留了原HLLC格式低耗散性的优点。     

滑坡支挡结构荷载取值问题研究

当前,在我国工程界,滑坡支挡结构上的荷载取值普遍以传递系数法的条间力(即剩余下滑力)为基础,本文对这种荷载取值方法存在的问题进行了分析,提出了以稳定性为基础确定滑坡支挡结构上荷载的方法,该方法能弥补现行荷载取值方法的不足。     

岩体变形参数渐变取值模型及工程应用

分析了当前岩体现场试验、变形参数取值和常规计算模式存在的问题。针对河谷、斜坡岩体从表部到深部 ,岩体风化、岩体波速和岩体地应力等彼此均呈现渐变性特征 ,提出了岩体变形参数渐变取值模型 ,并以黄河上游李家峡水电站初期蓄水监测资料 ,论证了岩体变形参数空间上连续性渐变取值的合理性和科学性 ,对今后其它岩体工程的力学参数取值和计算模型的概化提供了指导意义.     

边坡支护结构荷载取值问题研究

边坡支护结构上的荷载一般采用传统的土(岩)压力理论计算,本文对这种荷载取值方法存在的问题进行了分析,提出了以稳定性为基础确定边坡支挡结构上荷载的方法,该方法能弥补现行荷载取值方法的不足。     

用HLLC方法处理运动边界

针对含有运动边界非结构网格点的显式有限体积方法，研究了如何使用HLLC方法处理运动边界条件，计算了活塞拉伸、压缩问题，并和解析解进行了比较．作为应用示例，比较了静止圆柱绕流和静止流场中运动圆柱的绕流情形。结果表明：应用HLLC方法处理运动边界是可行的。     

Realization of contact resolving approximate Riemann solvers for strong shock and expansion flows

The Harten–Lax–van Leer contact (HLLC) and Roe schemes are good approximate Riemann solvers that have the ability to resolve shock, contact, and rarefaction waves. However, they can produce spurious solutions, called shock instabilities, in the vicinity of strong shock. In strong expansion flows, the Roe scheme can admit nonphysical solutions such as expansion shock, and it sometimes fails. We carefully examined both schemes and propose simple methods to prevent such problems. High‐order accuracy is achieved using the weighted average flux (WAF) and MUSCL‐Hancock schemes. Using the WAF scheme, the HLLC and Roe schemes can be expressed in similar form. The HLLC and Roe schemes are tested against Quirk's test problems, and shock instability appears in both schemes. To remedy shock instability, we propose a control method of flux difference across the contact and shear waves. To catch shock waves, an appropriate pressure sensing function is defined. Using the proposed method, shock instabilities are successfully controlled. For the Roe scheme, a modified Harten–Hyman entropy fix method using Harten–Lax–van Leer‐type switching is suggested. A suitable criterion for switching is established, and the modified Roe scheme works successfully with the suggested method. Copyright © 2009 John Wiley & Sons, Ltd.     

Study on the numerical schemes for hypersonic flow simulation

Hypersonic flow is full of complex physical and chemical processes, hence its investigation needs careful analysis of existing schemes and choosing a suitable scheme or designing a brand new scheme. The present study deals with two numerical schemes Harten, Lax, and van Leer with Contact (HLLC) and advection upstream splitting method (AUSM) to effectively simulate hypersonic flow fields, and accurately predict shock waves with minimal diffusion. In present computations, hypersonic flows have been modeled as a system of hyperbolic equations with one additional equation for non-equilibrium energy and relaxing source terms. Real gas effects, which appear typically in hypersonic flows, have been simulated through energy relaxation method. HLLC and AUSM methods are modified to incorporate the conservation laws for non-equilibrium energy. Numerical implementation have shown that non-equilibrium energy convect with mass, and hence has no bearing on the basic numerical scheme. The numerical simulation carried out shows good comparison with experimental data available in literature. Both numerical schemes have shown identical results at equilibrium. Present study has demonstrated that real gas effects in hypersonic flows can be modeled through energy relaxation method along with either AUSM or HLLC numerical scheme.     

一种简单的精确捕捉接触间断的黎曼求解器

基于Godunov型数值格式的有限体积法是求解双曲型守恒律系统的主流方法,其中用来计算界面数值通量的黎曼求解器在很大程度上决定了数值格式在计算中的表现。单波的Rusanov求解器和双波的HLL求解器具有简单、高效和鲁棒性好等优点,但是在捕捉接触间断时耗散太大。全波的HLLC格式能够精确捕捉接触间断,但是在计算中出现的激波不稳定现象限制了其在高马赫数流动问题中的应用。本文利用双曲正切函数和五阶WENO格式来重构界面两侧的密度值,并且结合边界变差下降算法来减小Rusanov格式耗散项中的密度差,从而提高格式对于接触间断的分辨率。研究表明,相比于全波的HLLC求解器,本文构造的黎曼求解器不仅具有更高的接触分辨率,而且还具有更好的激波稳定性。     

AUSM-like expression of HLLC and its all-speed extension

Advection upstream splitting method (AUSM) and Harten-Lax-van Leer with contact (HLLC) are two popular families of flux functions. The AUSM is simple and requires no eigenstructure, which facilitates its extensions to general equations of state. Furthermore, one of its variants, simple low-dissipation AUSM (SLAU), is applicable to all speeds and features removal of parameter setting by the user. HLLC, on the other hand, clearly defines three distinct waves in Riemann problem, namely, left-running and right-running acoustic waves, and entropy wave. This paper demonstrates that HLLC can be written in a very similar form with the AUSM family and that the similar manner in extending AUSM family to all speeds is easily incorporated into HLLC in this AUSM-like form. Then, we combine the strengths of the both flux functions and offer a new inviscid numerical flux function within the framework of monotone upwind scheme for conservation laws (MUSCL) in computational fluid dynamics (CFD) for Euler and Navier-Stokes equations. The resultant HLLC with low dissipation (HLLCL) numerical flux can compute low Mach number flows and sound propagations at the same time with high accuracy, as demonstrated by one-dimensional and two-dimensional numerical examples. Furthermore, the results indicate that its extensions to general fluids such as supercritical fluids are encouraging.     

AUFS 格式在无网格方法中的应用简

将计算量小,激波分辨率高的AUFS (artificially upstream flux vector splitting) 格式应用于无网格方法. 所发展算法基于多项式基函数最小二乘无网格方法,采用线性基函数曲面拟合及AUFS 格式计算各离散点的空间导数,应用四阶Runge-Kutta 法进行时间显式推进. 为验证算法健壮性、精度以及计算效率,对Riemann 问题、超音速平面流动,以及不同攻角NACA0012 翼型跨音速流场进行了数值模拟,其结果同采用HLLC (Harten-Lax-van Leer-contact) 格式的无网格方法以及文献报道结果吻合较好,并且计算量较形式简单HLLC 格式减少约15%.     

Energy relaxation method for chemical non‐equilibrium flow computations

In this paper, an algorithm for chemical non‐equilibrium hypersonic flow is developed based on the concept of energy relaxation method (ERM). The new system of equations obtained are studied using finite volume method with Harten–Lax–van Leer scheme for contact (HLLC). The original HLLC method is modified here to account for additional species and split energy equations. Higher order spatial accuracy is achieved using MUSCL reconstruction of the flow variables with van Albada limiter. The thermal equilibrium is considered for the analysis and the species data are generated using polynomial correlations. The single temperature model of Dunn and Kang is used for chemical relaxation. The computed results for a flow field over a hemispherical cylinder at Mach number of 16.34 obtained using the present solver are found to be promising and computationally (25%) more efficient. The present solver captures physically correct solution as the entropy conditions are satisfied automatically during the computations. Copyright © 2007 John Wiley & Sons, Ltd.     

MESHLESS METHOD FOR NUMERICAL SIMULATION OF SHOCK-INDUCED COMBUSTION

发展了基于无网格方法的激波诱导燃烧流场数值模拟算法. 该算法采用二维多组分Euler方程,在点云离散的基础上采用曲面逼近计算空间导数,引入多组分HLLC （Harten-Lax-van Leer-contact） 格式计算无黏通量,运用四阶Runge-Kutta 法进行时间显式推进,化学动力学采用有限速率反应模型. 对不同预混气体中的激波诱导燃烧流场进行了数值模拟,结果同相关文献吻合较好,验证了算法的正确性.