磁流体方腔槽道流整体线性稳定性数值方法研究

将Chebyshev谱配置法和基于非均匀网格的高阶FD-q差分格式运用于磁流体方腔槽道流整体线性稳定性研究,比较两类数值方法的优缺点.Chebyshev谱配置法收敛快且精度高,但需要构造非常庞大的满矩阵,存储量和计算开销巨大;高阶FD-q差分格式采用了基于Kosloff-Tal-Ezer变换的Chebyshev谱配置点作为离散网格,在保持较高网格收敛精度的同时,差分格式可以采用稀疏矩阵进行存储,显著降低了存储量和计算开销.相比传统的谱配置法,基于非均匀网格的高阶FD-q差分格式计算效率得到显著的提升,将高阶FD-q差分格式运用于非正则模线性最优瞬态增长的计算,计算效果良好.     

摄动有限体积法重构近似高精度的意义

研讨有限体积(FV)方法重构近似高精度的作用问题．FV方法中积分近似采用中点规则为二阶精度时，重构近似高精度(精度高于二阶)的意义和作用是一个有争议的问题．利用数值摄动技术构造了标量输运方程的积分近似为二阶精度、重构近似为任意阶精度的迎风型和中心型摄动有限体积(PFV)格式．迎风PFV格式无条件满足对流有界准则(CBC)，中心型PFV格式为正型格式，两者均不会产生数值振荡解．利用PFV格式求解模型方程的数值结果表明：与一阶迎风和二阶中心格式相比，PFV格式精度高、对解的间断分辨率高、稳定性好、雷诺数的适用范围大，数值地“证实”重构近似高精度和PFV格式的实际意义和好处．     

重新初始化的LS方法跟踪二维可压缩多介质流界面运动

 用非耦合求解方法计算Level Set函数方程与流体力学方程组，应用重新初始化的Level Set函数确保距离函数性质，流体力学方程组采用二阶精度多介质流波传播差分格式计算，重新初始化方程采用五阶WENO格式计算。并给出了二维可压缩多介质流界面运动的计算结果。     

不同负冲角工况下透平叶栅二次流的数值模拟及分析

本文应用TVD格式和Baldwin－Lomax代数紊流模型求解三维NS方程，对一个透平直列叶栅流场在两个不同的负冲角工况下进行了数值模拟，给出了叶栅马蹄涡及其分离鞍点、通道涡、角涡等二次流涡系的结构及其产生发展过程，并对不同工况下的涡系结构及冲角的影响作了详细的分析和比较．本文结果有助于对叶栅二次流涡系结构的产生发展机制的深入了解，同时表明所用数值求解技术有较高的精度和分辨率。     

有限雷诺数情况下微槽道可压缩流动滑移流模型稳定性的数值模似

通过对微槽道一阶滑移流模型稳定性的理论研究，发现在不可压缩流和雷诺数趋于零的情况下，当Knudsen数Kn大于1／9时，会出现不稳定现象．这一理论结论在可压缩流和有限雷诺数情况下是否成立，尚不清楚，采用成熟的计算方法，用数值计算来研究可压缩流和有限雷诺数情况下一阶滑移流模型的稳定性，发现随着雷诺数的减小，不稳定的临界Knudsen数也不断减小，逐渐趋近于在不可压缩流和雷诺数趋于零的情况下得到的理论分析结果。     

格子Boltzmann守恒型非平衡态的外推边界

针对非平衡态外推边界处理方法在某些条件下发生质量泄漏的问题,结合质量守恒定律对其进行修正,建立一种新的质量守恒型的边界处理格式.其基本思想是在边界处定义一个虚拟密度来修正平衡态分布函数,使得系统质量守恒.以重力作用下的密度场及磁流体模拟问题为例,利用该格式进行分析,讨论质量泄露问题的本质及各种因素的影响.通过对三种典型的流动:二维Poiseuille流、Couette流、Womersley流的模拟,验证该边界格式的计算精度和稳定性.     

混合通量差分格式的比较

系统研究了几种混合通量差分格式的构造方法和耗散模型,分别对低速平板绕流、二维跨音速喷管流动和高超音速钝头体无粘绕流进行了数值模拟,结合先进的EASM湍流模型对格式的粘性分辨率和激波稳定性进行了细致的比较分析.结果表明混合通量差分格式兼顾了FDS和FVS格式的优点,具有较高的间断分辨率和数值稳定性.     

基于树网格的格子Boltzmann方法以及曲线边界的处理

将格子玻尔兹曼方法(LBM)和BFECC技术相结合,在四叉树网格上实现,并用于二维不可压缩流动的求解.二维四叉树(三维八叉树)网格是一种非均匀网格,利用树结构进行数据存储,具有非常高的检索效率.BFECC是一种数值技巧,可以把求解输运方程的奇数阶格式通过误差修正提高一阶精度.基于四叉树网格的LBM,引入BFECC后,能有效减小输运过程中非均匀网格插值产生的误差,在总体上实现二阶精度,和经典的LBM方法相当.最后给出二维顶盖驱动方腔流动算例和二维圆柱绕流算例,从中可以看出格式的有效性.     

两类差分格式在锋生数值模拟中的应用比较

在二维理想锋生数值模式的基础上，用两类差分格式进行数值试验比较．计算结果表明，无论是在大气数值模拟中广泛使用的总能量守恒型差分格式，还是在高速流中捕捉接触间断较好的反扩散格式，对锋生过程均有较好的模拟能力，反扩散格式的效果更好一些．     

格子Boltzmann方法中的边界条件

比较并讨论了几种格子Boltzmann方法(LBM)中的边界条件处理方法，对标准的壁面全反弹方法进行了改进，提高了壁面反弹方法的精度．通过采用d2q9模型对Poiseuille流和非定常Coueue流进行数值模拟，获得了与分析解比较吻合的结果．针对不同的松弛时间τ和Re数，还给出了采取不同边界条件处理时的收敛精度，验证了小Re数时，LBM可以完全模拟N-S方程，由计算发现松弛时间τ接近1时的精度最高，τ较大时，误差较大。     

核探测器中混合气配制新方法

以质量流敏感器件和系统控制器为主要部件,建立起一套新的混合气配制系统,其配比误差小于满量程的1%,动态响应时间小于3s,有很好的长期稳定性,能满足核探测器对混合气体的多种需要.     

Enhanced linearized reduced-order models for subsurface flow simulation

Trajectory piecewise linearization (TPWL) represents a promising approach for constructing reduced-order models. Using TPWL, new solutions are represented in terms of expansions around previously simulated (and saved) solutions. High degrees of efficiency are achieved when the representation is projected into a low-dimensional space using a basis constructed by proper orthogonal decomposition of snapshots generated in a training run. In recent work, a TPWL procedure applicable for two-phase subsurface flow problems was presented. The method was shown to perform well for many cases, such as those with no density differences between phases, though accuracy and robustness were found to degrade in other cases. In this work, these limitations are shown to be related to model accuracy at key locations and model stability. Enhancements addressing both of these issues are introduced. A new TPWL procedure, referred to as local resolution TPWL, enables key grid blocks (such as those containing injection or production wells) to be represented at full resolution; i.e., these blocks are not projected into the low-dimensional space. This leads to high accuracy at selected locations, and will be shown to improve the accuracy of important simulation quantities such as injection and production rates. Next, two techniques for enhancing the stability of the TPWL model are presented. The first approach involves a basis optimization procedure in which the number of columns in the basis matrix is determined to minimize the spectral radius of an appropriately defined amplification matrix. The second procedure incorporates a basis matrix constructed using snapshots from a simulation with equal phase densities. Both approaches are compatible with the local resolution procedure. Results for a series of test cases demonstrate the accuracy and stability provided by the new treatments. Finally, the TPWL model is used as a surrogate in a direct search optimization algorithm, and comparison with results using the full-order model demonstrates the efficacy of the enhanced TPWL procedures for this application.     

High-order non-uniform grid schemes for numerical simulation of hypersonic boundary-layer stability and transition

The direct numerical simulation of receptivity, instability and transition of hypersonic boundary layers requires high-order accurate schemes because lower-order schemes do not have an adequate accuracy level to compute the large range of time and length scales in such flow fields. The main limiting factor in the application of high-order schemes to practical boundary-layer flow problems is the numerical instability of high-order boundary closure schemes on the wall. This paper presents a family of high-order non-uniform grid finite difference schemes with stable boundary closures for the direct numerical simulation of hypersonic boundary-layer transition. By using an appropriate grid stretching, and clustering grid points near the boundary, high-order schemes with stable boundary closures can be obtained. The order of the schemes ranges from first-order at the lowest, to the global spectral collocation method at the highest. The accuracy and stability of the new high-order numerical schemes is tested by numerical simulations of the linear wave equation and two-dimensional incompressible flat plate boundary layer flows. The high-order non-uniform-grid schemes (up to the 11th-order) are subsequently applied for the simulation of the receptivity of a hypersonic boundary layer to free stream disturbances over a blunt leading edge. The steady and unsteady results show that the new high-order schemes are stable and are able to produce high accuracy for computations of the nonlinear two-dimensional Navier–Stokes equations for the wall bounded supersonic flow.     

Flow difference effect in the two-lane lattice hydrodynamic model

By introducing a flow difference effect, a modified lattice two-lane traffic flow model is proposed, which is proved to be capable of improving the stability of traffic flow. Both the linear stability condition and the kink-antikink solution derived from the modified Korteweg-de Vries (mKdV) equation are analyzed. Numerical simulations verify the theoretical analysis. Furthermore, the evolution laws under different disturbances in the metastable region are studied.     

Sub-iteration leads to accuracy and stability enhancements of semi-implicit schemes for the Navier–Stokes equations

We present an iterative semi-implicit scheme for the incompressible Navier–Stokes equations, which is stable at CFL numbers well above the nominal limit. We have implemented this scheme in conjunction with spectral discretizations, which suffer from serious time step limitations at very high resolution. However, the approach we present is general and can be adopted with finite element and finite difference discretizations as well. Specifically, at each time level, the nonlinear convective term and the pressure boundary condition – both of which are treated explicitly in time – are updated using fixed-point iteration and Aitken relaxation. Eigenvalue analysis shows that this scheme is unconditionally stable for Stokes flows while numerical results suggest that the same is true for steady Navier–Stokes flows as well. This finding is also supported by error analysis that leads to the proper value of the relaxation parameter as a function of the flow parameters. In unsteady flows, second- and third-order temporal accuracy is obtained for the velocity field at CFL number 5–14 using analytical solutions. Systematic accuracy, stability, and cost comparisons are presented against the standard semi-implicit method and a recently proposed fully-implicit scheme that does not require Newton’s iterations. In addition to its enhanced accuracy and stability, the proposed method requires the solution of symmetric only linear systems for which very effective preconditioners exist unlike the fully-implicit schemes.     

基于大涡模拟的移动粒子半隐式算法

移动粒子半隐式方法(MPS)是一种粒子方法,多用于模拟带有自由表面的不可压缩流动。工程实际中的自由表面流动往往是复杂的湍流流动,本文借鉴网格类方法的亚格子应力模型发展了基于Smagorinsky模型的亚粒子应力模型,并将其耦合到MPS方法中,实现了基于大涡模拟的MPS方法并用于研究自由表面湍流问题。为了提高计算的准确性和稳定性,SPS模型中出现的一阶导数项采用最小二乘法拟合得到,SPS项采用显式算法进行计算。使用这一算法模拟了溃坝问题,结果表明,采用亚粒子应力模型的模拟结果与实验的吻合程度明显提高。     

基于随机子空间结合稳定图的气液两相流型分析

研究了几种典型气液两相流流型的稳定图特征,并应用随机子空间方法对47种流动条件下的流型 信号进行了识别.研究结果表明:稳定图特征能够反映出复杂时间序列的内部特征,利用其提取的直线度特征 值可以对时间序列的特征进行量化分析,三种典型流型的稳定图特征差异较明显,泡状流的稳定图特征最为 混乱,雾状流次之,段塞流最为规整.应用随机子空间方法对气液两相流图像灰度波动序列进行特征向量提取 和辨识,通过幅值以及相角的分布特征能够对不同工况下的流型样本进行准确分类,为多相流的分类提供了 一条新路径.同时基于稳定图的分析方法为进一步揭示多相流的流动机理提供有益的探索.     

Flow difference effect in the lattice hydrodynamic model

In this paper,a new lattice hydrodynamic model based on Nagatani’s model [Nagatani T 1998 Physica A 261 599] is presented by introducing the flow difference effect.The stability condition for the new model is obtained by using the linear stability theory.The result shows that considering the flow difference effect leads to stabilization of the system compared with the original lattice hydrodynamic model.The jamming transitions among the freely moving phase,the coexisting phase,and the uniform congested phase are studied by nonlinear analysis.The modified KdV equation near the critical point is derived to describe the traffic jam,and kink-antikink soliton solutions related to the traffic density waves are obtained.The simulation results are consistent with the theoretical analysis for the new model.     

Nonlinear analysis of traffic jams in an anisotropic continuum model

This paper presents our study of the nonlinear stability of a new anisotropic continuum traffic flow model in which the dimensionless parameter or anisotropic factor controls the non-isotropic character and diffusive influence.In order to establish traffic flow stability criterion or to know the critical parameters that lead,on one hand,to a stable response to perturbations or disturbances or,on the other hand,to an unstable response and therefore to a possible congestion,a nonlinear stability criterion is derived by using a wavefront expansion technique.The stability criterion is illustrated by numerical results using the finite difference method for two different values of anisotropic parameter.It is also been observed that the newly derived stability results are consistent with previously reported results obtained using approximate linearisation methods.Moreover,the stability criterion derived in this paper can provide more refined information from the perspective of the capability to reproduce nonlinear traffic flow behaviors observed in real traffic than previously established methodologies.     

Airflow measurements: Theory and utility of findings

The biomechanical movements of vocal structures are shown to control flow of expiratory air for the production of speech sounds. Laminar and turbulent air flow are discussed as they relate to sound generation. Theoretic and therapeutic utility of air flow profiles in differentiating linguistic contrasts and vocal characteristics are discussed along with considerations of relative utility and accuracy for various flow-measuring devices and strategies.