应用于计算气动声学的优化有限紧致格式

对于含间断的计算气动声学问题,数值计算的格式不仅要求低耗散低色散的设计,对短波具有较高的分辨率,还要求能捕捉激波.中心紧致格式具有高精度,具有无耗散和低色散特征,但不能捕捉间断和激波;WENO格式处理间断较为成功,而耗散和色散误差相对较大.有限紧致格式可以将紧致格式与WENO格式相结合构造成混合格式,利用光滑因子之间的关系对激波区域进行自动判断,将传统的全域求解的紧致格式划分为有限的局部紧致求解,间断点上的激波捕捉铜梁自动作为局部紧致求解的边界通量,在在光滑区域具有紧致格式的高精度低耗散性质,在激波附近不产生非物理振荡.本文利用有限紧致格式思想,构造了新的适合于气动声学问题的优化有限紧致格式,将其应用于计算气动声学一维标准测试问题,对相关格式的模拟性能进行了评估,显示该格式在宽频声波传播和含有间断的声波传播模拟方面具有优势.     

An Adaptive Grid Eulerian Method for the Computation of Free Surface Flows

A numerical scheme for the prediction of free surface flows is presented and investigated. The method is based on an adaptive grid Eulerian finite-volume method, where non-orthogonal boundary-fitted moving grids are employed to follow the free surface. The underlying flow solver consists in a pressure-correction scheme of SIMPLE type with multigrid acceleration, which is iteratively combined with the moving grid technique. Several numerical examples are considered to illustrate the capabilities of the approach.     

Two-stage fourth-order gas-kinetic scheme for three-dimensional Euler and Navier-Stokes solutions

ABSTRACT

For the one-stage third-order gas-kinetic scheme (GKS), successful applications have been achieved for the three-dimensional compressible flows [Pan, L., K. Xu, Q. Li, and J. Li. 2016. “An Efficient and Accurate Two-stage Fourth-order Gas-kinetic Scheme for the Navier-Stokes Equations.” Journal of Computational Physics 326: 197–221]. The high-order accuracy of the scheme is obtained by integrating a multidimensional time-accurate gas distribution function over the cell interface within a time step without using Gaussian quadrature points and Runge-Kutta time-stepping technique. However, to the further increase of the order of the scheme, such as the fourth-order one, the one step formulation becomes very complicated for the multidimensional flow. Recently, a two-stage fourth-order GKS with high efficiency has been constructed for two-dimensional inviscid and viscous flow computations ([Li, J., and Z. Du. 2016. “A Two-stage Fourth Order Time-accurate Discretization for Lax-Wendroff Type Flow Solvers I. Hyperbolic Conservation Laws.” SIAM Journal on Scientific Computing 38: 3046–3069]; Pan et al. 2016), and the scheme uses the time accurate flux function and its time derivatives. In this paper, a fourth-order GKS is developed for the three-dimensional flows under the two-stage framework. Based on the three-dimensional WENO reconstruction and flux evaluation at Gaussian quadrature points on a cell interface, the high-order accuracy in space is achieved first. Then, the two-stage time stepping method provides the high accuracy in time. In comparison with the formal third-order GKS [Pan, L., and K. Xu. 2015. “A Third-order Gas-kinetic Scheme for Three-dimensional Inviscid and Viscous Flow Computations.” Computers & Fluids 119: 250–260], the current fourth-order method not only improves the accuracy of the scheme, but also reduces the complexity of the gas-kinetic flux solver greatly. More importantly, the fourth-order GKS has the same robustness as the second-order shock capturing scheme [Xu, K. 2001. “A Gas-kinetic BGK Scheme for the Navier-Stokes Equations and its Connection with Artificial Dissipation and Godunov Method.” Journal of Computational Physics 171: 289–335]. Numerical results validate the outstanding reliability and applicability of the scheme for three-dimensional flows, such as the cases related to turbulent simulations.     

On the Accuracy of Upwind and Symmetric TVD Schemes in Simulating Low Mach Number Flow

The accuracy of MUSCL upwind and Yee-Roe-Davis symmetric TVD schemes for simulating low Mach number flow is studied through a numerical experiment of the 2-D lid driven cavity problem. The steady slate solution is reached by using a marching approach based on the pseudocompressibilty method in conjunction with implicit approximate factorization. A finite volume discretization of the conservation equations is used with a four level multigrid method to accelerate the convergence. The tests performed which were in the range of 100 ≤ Re ≤ 5000, show that the Yee-Roe-Davis symmetric scheme generates results in very good agreement with the benchmark results over this range of Re. The MUSCL upwind scheme accuracy deteriorates with the increasing Re.     

一维守恒的Lagrangian ADER格式

基于欧拉框架下ADER格式,构造一维守恒只有一个时间步的、高精度中心型拉格朗日ADER(LADER)格式.构造r阶LADER格式包括:从欧拉方程出发推导拉格朗日框架下积分形式的方程、采用WENO方法高精度重构节点处守恒量和从1阶到r-1阶的空间导数、求拉氏框架下这些变量的Godunov值,并计算1阶到r-1阶的时间全导数,最后高精度离散积分形式的流通量函数.对光滑流场的模拟表明,LADER格式达到设计的精度;对含强间断的流场模拟表明,数值解在间断附近基本无振荡.     

Piezoelectric transducer parameter selection for exciting a single mode from multiple modes of Lamb waves

Excitation and propagation of Lamb waves by using rectangular and circular piezoelectric transducers surface-bonded to an isotropic plate are investigated in this work. Analytical stain wave solutions are derived for the two transducer shapes, giving the responses of these transducers in Lamb wave fields. The analytical study is supported by a numerical simulation using the finite element method. Symmetric and antisymmetric components in the wave propagation responses are inspected in detail with respect to test parameters such as the transducer geometry, the length and the excitation frequency. By placing only one piezoelectric transducer on the top or the bottom surface of the plate and weakening the strength of one mode while enhancing the strength of the other modes to find the centre frequency, with which the peak wave amplitude ratio between the S0 and A0 modes is maximum, a single mode excitation from the multiple modes of the Lamb waves can be achieved approximately. Experimental data are presented to show the validity of the analyses. The results are used to optimize the Lamb wave detection system.     

利用小行星视线矢量的火星探测光学自主导航研究

结合我国即将开展的自主火星探测计划,研究了航天器在火星探测巡航过程中利用小行星进行光学自主导航的整个过程. 根据巡航段的设计轨道,给出了导航小行星的筛选条件并筛选出可用于实际任务的导航小行星序列. 将自主导航的数据弧段长度设定为30d,数据观测周期为5d. 采用加权最小二乘滤波算法,当数据弧段长度为30d时,导航计算的位置误差在100～400km变化,速度误差不超过0.25m/s.      

Lagrange方法基于保正性的时间步长

对交错网格上Lagrange预估-校正显示格式的时间步长选取提出新的方法.与经典CFL稳定性理论时间步长选取方法不同,新方法考虑了原始微分方程组的非线性效应,并基于物理量保正性给出了自适应的时间步长选取方法.数值实验验证了该方法有效.     

Synchronization of impulsively coupled complex networks

We investigate the synchronization of complex networks,which are impulsively coupled only at discrete instants.Based on the comparison theory of impulsive differential systems,a distributed impulsive control scheme is proposed for complex dynamical networks to achieve synchronization.The proposed scheme not only takes into account the influence of all nodes to network synchronization,which depends on the weight of each node in the network,but also provides us with a flexible method to select the synchronized state of the network.In addition,it is unnecessary for the impulsive coupling matrix to be symmetrical.Finally,the proposed control scheme is applied to a chaotic Lorenz network and Chua’s circuit network.Numerical simulations are used to illustrate the validity of this control scheme.     

High-order numerical methods of fractional-order Stokes’ first problem for heated generalized second grade fluid

The high-order implicit finite difference schemes for solving the fractionalorder Stokes’ first problem for a heated generalized second grade fluid with the Dirichlet boundary condition and the initial condition are given. The stability, solvability, and convergence of the numerical scheme are discussed via the Fourier analysis and the matrix analysis methods. An improved implicit scheme is also obtained. Finally, two numerical examples are given to demonstrate the effectiveness of the mentioned schemes.