应用随机模型方法预测汽车风噪声

采用随机模型方法,对简化汽车头部外形进行风噪声数值模拟.将计算区域分为声源区域和传播区域,在声源区域采用随机模型构造湍流脉动速度场,传播区域通过求解带源项的线化欧拉方程实现声波向外传播得到声场解.同直接模拟方法相比,该方法具有计算量小、计算所需内存少等优点.数值模拟结果与实验数据吻合较好,验证了该方法预测汽车风噪声的可行性,为研究实际汽车外形的风噪声问题打下基础.     

方柱绕流大涡模拟

采用有限体/有限元混合格式、非结构网格和大涡模拟方法求解可压缩的N-S方程,对Re=22 000的方柱绕流进行数值模拟,并对不同的边界条件进行详细的分析比较.通过对以往研究经验的总结和利用精细的边界条件,使得采用二阶精度的数值格式和较稀疏的网格仍然得到了令人满意的计算结果,甚至优于以往采用密网格的模拟结果.     

时域有限差分法在建筑声学中的应用及前景

介绍了声波方程的基本差分格式及稳定条件、数值色散、吸收边界条件等数值计算理论，例举了前人用时域有限差分法对噪声传播过程的模拟和室内声学中座椅吸声低谷效应模拟的模拟结果。本文指出，由于时域有限差分法的特点使其具有在模拟脉冲响应方而的特别优势，因而，应用这一技术研究厅堂的声学特性，尤其是低频特性，将有重要意义。     

快速随机粒子网格法的气动噪声预测方法

耦合随机湍流速度生成模型与线化欧拉方程技术,形成了一套具备模拟噪声在非均匀流场中传播能力的气动噪声混合预测方法。该混合方法的随机湍流速度生成模型采用了快速随机粒子网格法,为声传播模拟提供了可靠的源项。而噪声的传播计算选用线化欧拉方程,其空间离散采用9点5阶的色散保持关系格式,时间推进选用了高精度大时间步长的6级4阶龙格库塔格式,远场边界应用了无分裂形式的理想匹配层边界条件。首先,选用高斯脉冲传播算例对线化欧拉方程的时空离散格式、远场无反射边界条件进行了验证分析。然后,计算分析各向同性湍流的空间相关性验证湍流速度生成模型的可靠性。最后,基于已搭建的气动噪声混合预测方法进行了30P30N三段翼缝翼噪声的计算分析。计算分析可知:监测点处功率谱密度曲线、噪声指向性等计算结果与参考文献结果取得了较好的一致性。数值计算结果表明所建立的气动噪声混合预测方法能有效预测二维复杂构型的气动噪声问题。      

基于非结构网格CE/SE算法圆柱绕流气动声场模拟

本文采用时空守恒(CE/SE)格式求解Navier-Stoks方程与Euler方程,数值模拟了绕圆柱流动引发的气动噪声源及传播问题.对近声场与远声场采用了不同的控制方程和边界条件,分别得到了流场与声场解.将其与采用大涡模拟和FW-H方程得到的结果进行了对比,表明本文的数值方法能够很好地反映流场与声场的形态,能较好地模拟声场指向性及流场中的拟声现象,相比LES/FW-H方法能更精确地反映流场与声场的相互关系.     

机翼后缘噪声预测研究

机翼后缘噪声是飞机重要的机体噪声源之一。本文基于CFD(Computational Fluid Dynamic)数值模拟和Ffcows Williams-Hall理论,研究应用了一种预测干净机翼后缘气动噪声的方法。采用Menter’s SSTκ-ω湍流模型对翼型和机翼进行N-S方程数值模拟得到后缘附近的湍流特征速度和特征长度,再利用Serhat Hosder的预估方法计算后缘噪声强度级。本文首先计算了NACA0012翼型在7种不同状态的后缘噪声,计算结果与实验值比较,符合很好,从而证明了本文采用的方法的可行性和正确性;然后研究了两个亚音速翼型(NACA 0009,NACA 0012),两个超临界翼型(SC(2)- 0710,SC(2)-0714),EET机翼的不同参数对后缘噪声强度级的影响,得出了对降低后缘噪声有参考意义的结论。     

高精度有限差分法模拟Kelvin-Helmholtz不稳定性

 WENO有限差分格式有较高的分辨精度,适合复杂流场的计算,在国际上被广泛采用。本文利用WENO有限差分格式求解2维守恒型欧拉方程,实现了对无粘流体中Kelvin-Helmholtz不稳定性的数值模拟。速度剪切方向采用周期边界条件;扰动增长方向采用嵌边出流边界条件,一个不稳定波长分布64个网格。数值模拟给出的扰动幅值线性增长率与线性稳定性分析给出的结果很好符合,显示了该格式的有效性和精度。数值模拟给出了清晰的密度等值线,表明该方法还具有较好的界面变形捕捉能力。     

蒙特卡罗方法在解微分方程边值问题中的应用

介绍了蒙特卡罗方法的基本原理以及随机数的产生方法。基于蒙特卡罗方法的思想,结合有限差分方法,建立了求解微分方程边值问题的随机概率模型,并以第一类边界条件的拉普拉斯方程和一个给定初值及边界条件的非稳态热传导方程为数值算例,研究了蒙特卡罗方法在求解微分方程边值问题中的应用。结果表明:利用蒙特卡罗方法,不仅可以有效解决给定边界条件的微分方程,对于给定初值条件的微分方程,也可以从时域有限差分方程出发,采用蒙特卡罗方法进行求解。数值模拟和对误差的理论分析均表明,增加蒙特卡罗试验中的模拟粒子点数,可以提高计算结果的精度。     

Rijke管自激热声振荡的数值模拟

为了对热声不稳定的发生及控制机理进行研究,对Rijke管内的自激热声振荡现象进行了数值模拟。采用具有低频散低耗散特点的计算气动声学方法,对带有非线性热源项的声波方程进行数值求解,并比较了不同的热源模型及边界条件对非线性效应的影响。结果表明,计算气动声学方法可以成功捕捉到Rijke管内压力的起振过程,而且在速度扰动达到平均流速度的1/3时,振荡会由线性增长转为非线性增长,最终达到有限幅值极限循环。相比热源项,考虑管口辐射耗散的非线性边界条件在振荡幅值和频谱方面对结果的影响都比较小。数值模拟得到的结果与实验符合较好,表明计算气动声学方法适合于热声振荡问题的研究。      

A Direct Discontinuous Galerkin Method for Nonlinear Schr(o)dinger Equation

讨论一维和二维非线性Schr(o)dinger (NLS)方程的数值求解.基于扩散广义黎曼问题的数值流量,构造一种直接间断Galerkin方法(DDG)求解非线性Schr(o)dinger方程.证明该方法L2稳定性,并说明DDG格式是一种守恒的数值格式.对一维NLS方程的计算表明,DDG格式能够模拟各种孤立子形态,而且可以保持长时间的高精度.二维NLS方程的数值结果显示该方法的高精度和捕捉大梯度的能力.     

两相湍流色噪声扩维法PDF模型及数值模拟

由颗粒运动的朗之万方程出发,对流体脉动速度采用扩维方法,得到两个不同层次的PDF输运方程.通过对颗粒运动方程求解和高斯分布假设,解决PDF方程的封闭问题,获得颗粒二阶矩模型,然后将颗粒应力方程简化成代数方程,建立代数应力模型.将对流扩散方程的有限分析法运用到求解两相流模型中,对壁面两相射流进行数值模拟,对比分析数值结果与实验结果.     

随机微分方程计算方法及其应用

介绍随机微分方程离散化格式的构造、收敛性法则、强收敛格式、弱收敛格式、带跳跃的随机微分方程的计算方法,偏微分方程的概率求解以及它们在物理、工程和金融等领域中的一些应用.     

Stability of Exponential Euler Method for Stochastic Systems under Poisson White Noise Excitations

The stability of stochastic systems under Poisson white noise excitations which based on the quantum theory is investigated in this paper. In general, the exact solution of the most of the stochastic systems with jumps is not easy to get. So it is very necessary to investigate the numerical solution of equations. On the one hand, exponential Euler method is applied to study stochastic delay differential equations, we can find the sufficient conditions for keeping mean square stability by investigating numerical method of systems. Through the comparison, we get the step-size of this method which is longer than the Euler-Maruyama method. On the other hand, mean square exponential stability of exponential Euler method for semi-linear stochastic delay differential equations under Poisson white noise excitations is confirmed.     

Thin-Film Flow Influenced by Thermal Noise

We study the influence of thermal fluctuations on the dewetting dynamics of thin liquid films. Starting from the incompressible Navier-Stokes equations with thermal noise, we derive a fourth-order degenerate parabolic stochastic partial differential equation which includes a conservative, multiplicative noise term—the stochastic thin-film equation. Technically, we rely on a long-wave-approximation and Fokker–Planck-type arguments. We formulate a discretization method and give first numerical evidence for our conjecture that thermal fluctuations are capable of accelerating film rupture and that discrepancies with respect to time-scales between physical experiments and deterministic numerical simulations can be resolved by taking noise effects into account.     

Noise transmission through stiffened panels

An analytical study is presented to predict low frequency noise transmission through finite stiffened panels into rectangular enclosures. Noise transmission is determined by solving the acoustic wave equation for the interior noise field and stiffened panel equations for vibrations of panels and stringers. The solution to this system of equations is obtained by a Galerkin-like procedure where the modes and frequencies for stiffened panels are determined by the transfer matrix method. Results include a comparison between theory and experiment and noise transmission through the sidewall of an aircraft.     

Numerical analysis of uncertain temperature field by stochastic finite difference method

Based on the combination of stochastic mathematics and conventional finite difference method,a new numerical computing technique named stochastic finite difference for solving heat conduction problems with random physical parameters,initial and boundary conditions is discussed.Begin with the analysis of steady-state heat conduction problems,difference discrete equations with random parameters are established,and then the computing formulas for the mean value and variance of temperature field are derived by the second-order stochastic parameter perturbation method.Subsequently,the proposed random model and method are extended to the field of transient heat conduction and the new analysis theory of stability applicable to stochastic difference schemes is developed.The layer-by-layer recursive equations for the first two probabilistic moments of the transient temperature field at different time points are quickly obtained and easily solved by programming.Finally,by comparing the results with traditional Monte Carlo simulation,two numerical examples are given to demonstrate the feasibility and effectiveness of the presented method for solving both steady-state and transient heat conduction problems.     

Probability Density and Joint Probability Density of SDE with General Nonlinear Gaussian Noise

We consider a stochastic differential equation with a general nonlinearity in Gaussian noise; With both D (fluctuation intensity) and γ (correlation time) small quantities with D/γ < 1/10, approximate equations for the probability density p(q, t) and the joint probability density p(q, t, q^t, t^p) are derived. As applications of our general equations, quadratic noise, exponential noise and triangle function noise are studied.