三维非结构网格Euler方程的LU-SGS算法及其改进

将LU-SGS隐式时间推进格式运用到非结构网格Euler方程的求解中,并对传统LU-SGS格式进行改进,结合网格重排序,发展了一套效率更高的三维Euler方程求解器.以M6机翼及超临界LANN机翼的跨音速无粘流场为算例,将改进LU-SGS格式与四步龙格-库塔显式格式及传统LU-SGS格式进行了比较.计算结果表明:所有格式的计算结果与实验结果都符合很好;传统LU-SGS格式计算效率为显式格式的3倍多,而改进LU-SGS格式计算效率为显式格式的7倍多.     

振荡叶栅非定常流场的N-S方程解

本文采用直接解N-S方程的方法求解振荡叶栅的非定常流场.数值格式采用MC-LB显隐格式,时间步长可以取得较大,故总计算时间并不比用显格式直接解Euler方程长很多.计算结果与无粘结果基本一致.但来流时均静压比定常来流静压略有提高,这是与无粘计算不同之处.     

间断有限元方法在弹尾超音速喷流计算中的应用

采用间断有限元方法对超音速无粘喷流流动进行数值模拟.将二维双曲守恒方程的间断有限元方法发展到轴对称Euler方程,并就某导弹尾部超音速伴随射流进行数值计算.计算结果与实验照片反映的流动特征吻合较好,与高精度、高分辨率TVD格式的计算结果相比,间断有限元方法的计算结果在轴线反射点附近具有较高的分辨率,表明该方法对激波具有较强的捕捉能力,在激波阵面上不会产生振荡或抹平间断现象.     

一种基于AUSM思想的通量分裂方法

根据对流迎风分裂(AUSM)思想提出一种通量分裂方法,称为K-CUSP格式.它与传统H-CUSP和E-CUSP格式的最大差异在于总能量的分裂:K-CUSP格式将无粘守恒通量中所有的运动学量分裂到对流项,所有的热力学量分裂到压力项,即总能量被分裂成动能和静焓.对于压力项的数值通量,采用一种新的界面构造方法.数值测试表明:①K-CUSP格式继承了FVS格式的简单性和稳健性.在激波后不易出现压力过冲,在膨胀区域没有振荡,优于AUSM和WPS格式;②K-CUSP格式继承了FDS格式的分辨率.激波间断的分辨率和H-CUSP、E-CUSP格式基本相同,接触间断的分辨率高于FVS格式,低于Roe、AUSM和WPS格式.AUSM和WPS格式在计算运动接触间断时,速度存在很大振荡,而新格式不存在振荡.     

数值求解Navier-Stokes方程的一个新的系数矩阵分裂法

在一个单步格式的基础上构造了一个新的隐式系数矩阵分裂法来数值求解可压Navier-St-okes方程。对方程中的无粘项部分利用守恒型方程中流通量向量为一齐次函数这一特性,根据Jacobian矩阵特征值的符号而将流通向量分裂成两部分。在此基础上据风向而构造逼近于无粘项的差分格式。对方程中的粘性项部分利用算子附加修正的方法来改进计算的收敛过程。所建立的差分格式被用来数值求解Couette流以考查这一方法。     

N-S方程隐式分区并行计算

将Wu Z N和Zou H提出的一套适合三点块三对角隐式格式的定常和非定常可压无粘流的覆盖分区并行计算方法推广到N-S方程的计算.在二维定常亚音速、跨音速和非定常情况下都得到了较好的绝对并行效率.     

采用Power限制器的PNND和PWNND格式

为高精度捕捉激波等流场结构,引入一种Power限制器,对NND格式和WNND格式进行改进,分别得到二阶PNND(Power NND)格式和三阶PWNND(Power WNND)格式.该Power类型格式通过Power限制器对相邻待选模板上的一阶导数进行限制,改善了NND格式和WNND格式在间断附近的耗散效应.对各种格式的分析表明,在间断附近采用Power限制器的格式比原格式的表现要好,耗散小且捕捉间断精度高,其中PNND格式虽然只有二阶精度,但在所有算例中与三阶WNND格式的计算结果比较接近,在个别算例中甚至优于WNND格式.最后将PWNND格式应用到二维NACA0012翼型的强迫俯仰振动的数值模拟,计算结果与实验值、参考计算值吻合较好.     

Ghost Fluid方法与双介质可压缩流动计算

应用带有Isobaric修正的GhostFluid方法配合LevelSet方法计算可压缩双介质无粘流动.该方法可以消除计算流体界面时所产生的数值跳动和耗散,且编程上比界面跟踪法简单.应用WENO格式数值求解欧拉方程和LevelSet方程,对由刚性气体状态方程所支配的一二维双介质流动进行数值计算,得到了分辨率较高的计算结果.     

不规则对接网格的分区求解计算

采用一种保持通量守恒的不规则对接网格分区求解中交界面耦合条件的计算方法, 结合有限体积法求解了Euler 方程, 无粘通量取用Van Leer 分裂格式, 构造了一种限制器以实现格式的二阶精度和TVD 性质, 并给出数值算例。     

求解Euler方程的高精度的空间--时间守恒格式

空间-时间守恒(STC)格式是近年来发展出的一种计算格式,在现有的STC格式构造过程中,流动变量在解元中的分布都用其一阶Taylor展开式来表示.STC格式的精度与所采用的Taylor展开式的阶数有关.该文采用流动变量的二阶Taylor展开式来表示其在解元上的分布、构造出了求解一维Euler方程的STC格式.用该格式对几个问题进行了计算,将计算结果与精确解进行了比较,比较表明该格式有较高的精度.     

运动涡旋脉冲引起的光学畸变

 主要研究了气动噪声对光传输和成像的影响。流场求解采用法福尔平均N-S方程，并分别利用基于MUSCL格式的AUSMPW+分裂和二阶中心格式对流通量和粘性通量进行离散处理；用四步四阶Runge-Kutta格式对方程进行时间推进求解，采用J-B两方程模型并经Sarkar方法进行可压缩修正后用于湍流的数值模拟。采用基于光学传递函数的物理光学方法分析平均流动和湍流对光质的影响。研究表明：涡脉冲在运动过程中会引起光束沿涡脉冲运动方向产生较大的整体偏折，偏折幅度随时间而变，最大偏折幅度可以达到1.7 μrad；在与涡脉冲运动的垂直方向，整体偏折基本可以忽略不记。在涡脉冲横穿光束的过程中，平均流动会导致焦平面光强峰值有两次下降，平均流动对光强重新分布的影响比湍流脉动影响更强。涡脉冲在运动过程中，先导致光束能量在与涡脉冲运动垂直的方向上扩散，随后使之在涡脉冲运动方向上向外转移。因能量向外扩散，导致Strehl比在0.9 s时刻降低到0.60左右。     

双曲型守恒律的一种三阶半离散中心迎风格式

对一维双曲型守恒律,给出了一种具有较小数值耗散的三阶半离散中心迎风格式.该格式以Liu和Tadmor提出的三阶无振荡重构为基础,同时考虑了波传播的单侧局部速度.时间离散用保持强稳定性的三阶Runge-Kutta方法.由于不需用Riemann解算器,避免了特征分解过程,保持了中心格式简单的优点.数值算例验证本方法可进一步减小数值耗散,提高分辨率.     

黏性激波管的有限体积WENO格式数值模拟

本文采用OpenFOAM软件下实现的一种可实现任意阶数,可应用于非结构网格的有限体积WENO格式对黏性激波管问题进行模拟。模拟中对流项离散采用3阶精度、4阶精度该类WENO格式,网格形式采用结构网格和三角形非结构网格。结果表明,采用该类格式,三角形非结构网格的算精度、效率优于结构网格,3阶精度格式计算效率优于4阶精度。该工作表明OpenFOAM下采用3阶精度该类格式及非结构网格对叶轮机械内部流动等复杂流场的模拟更具优势与应用潜力.     

Third-order ghost interference with thermal light

A scheme for third-order ghost interference with thermal light is proposed. The visibility and resolution of the interference fringe related to the bandwidth of the spatial frequency spectrum of the source are analysed. The results show that the visibility of the third-order ghost interference fringe is much higher than that of the second-order one.     

一种提高基于循环频移器的多载波光源光信噪比的方案

频率锁定多载波光源是实现太比特系统传输的关键器件之一, 目前已成为光纤通信领域的研究热点.基于循环频移技术产生的频率锁定 多载波光源因具有驱动电压低、串扰小、平坦度高的优点而受到重视, 但是其输出质量容易受到调制器固有的高阶谐波串扰的影响,特别是三阶谐波串扰. 为了减小三阶串扰的影响,本文提出了在I/Q调制器两支路上再加载另一频率为3f_m的射频信号的方案, 用其产生的一阶信号来抑制三阶串扰.通过理论分析与数值仿真,得到了载波数为24、 载波间最大功率差小于0.1 dB的多载波光源输出.与未采用三阶串扰抑制方案的结果比较, 光源输出有效光信噪比提高了2 dB. 结果表明,采用本文的改进方案,可以有效地提高多载波光源的输出平坦度和有效光信噪比.     

Third-order Energy Stable WENO scheme

A new third-order Energy Stable Weighted Essentially Non-Oscillatory (ESWENO) finite difference scheme for scalar and vector hyperbolic equations with piecewise continuous initial conditions is developed. The new scheme is proven to be linearly stable in the energy norm for both continuous and discontinuous solutions. In contrast to the existing high-resolution shock-capturing schemes, no assumption that the reconstruction should be total variation bounded (TVB) is explicitly required to prove stability of the new scheme. We also present new weight functions which drastically improve the accuracy of the third-order ESWENO scheme. Based on a truncation error analysis, we show that the ESWENO scheme is design-order accurate for smooth solutions with any number of vanishing derivatives, if its tuning parameters satisfy certain constraints. Numerical results show that the new ESWENO scheme is stable and significantly outperforms the conventional third-order WENO scheme of Jiang and Shu in terms of accuracy, while providing essentially non-oscillatory solutions near strong discontinuities.     

Numerical Study on the Performance in High-bit-rate Optical Communication Systems

By numerical simulations, we show that picosecond Gaussian optical pulses with a precise optimal frequency chirping can transmit stably in full-dispersion compensation optical fiber links, with not only second- but also third-order dispersion compensation, using dispersion shift fibers with opposite dispersion sign. The optimal pre-chirp is determined principally by the second-order dispersion scheme and scarcely affected by third-order dispersion scheme. It demonstrates that, to a high bit rate transmission system, the pre-chirping technology and higher-order dispersion compensation are two very efficient measures in improving performance of system.     

New Criteria on Oscillatory and Asymptotic Behavior of Third-Order Nonlinear Dynamic Equations with Nonlinear Neutral Terms

In the paper, we provide sufficient conditions for the oscillatory and asymptotic behavior of a new type of third-order nonlinear dynamic equations with mixed nonlinear neutral terms. Our theorems not only improve and extend existing theorems in the literature but also provide a new approach as far as the nonlinear neutral terms are concerned. The main results are illustrated by some particular examples.     

A multiple-relaxation-time lattice Boltzmann method for high-speed compressible flows

This paper presents a coupling compressible model of the lattice Boltzmann method. In this model, the multiplerelaxation-time lattice Boltzmann scheme is used for the evolution of density distribution functions, whereas the modified single-relaxation-time(SRT) lattice Boltzmann scheme is applied for the evolution of potential energy distribution functions. The governing equations are discretized with the third-order Monotone Upwind Schemes for scalar conservation laws finite volume scheme. The choice of relaxation coefficients is discussed simply. Through the numerical simulations,it is found that compressible flows with strong shocks can be well simulated by present model. The numerical results agree well with the reference results and are better than that of the SRT version.     

A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows

We extend [Shravan K. Veerapaneni, Denis Gueyffier, Denis Zorin, George Biros, A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D, Journal of Computational Physics 228(7) (2009) 2334–2353] to the case of three-dimensional axisymmetric vesicles of spherical or toroidal topology immersed in viscous flows. Although the main components of the algorithm are similar in spirit to the 2D case—spectral approximation in space, semi-implicit time-stepping scheme—the main differences are that the bending and viscous force require new analysis, the linearization for the semi-implicit schemes must be rederived, a fully implicit scheme must be used for the toroidal topology to eliminate a CFL-type restriction and a novel numerical scheme for the evaluation of the 3D Stokes single layer potential on an axisymmetric surface is necessary to speed up the calculations. By introducing these novel components, we obtain a time-scheme that experimentally is unconditionally stable, has low cost per time step, and is third-order accurate in time. We present numerical results to analyze the cost and convergence rates of the scheme. To verify the solver, we compare it to a constrained variational approach to compute equilibrium shapes that does not involve interactions with a viscous fluid. To illustrate the applicability of method, we consider a few vesicle-flow interaction problems: the sedimentation of a vesicle, interactions of one and three vesicles with a background Poiseuille flow.