λ算法在轴对称情况的改进

本文给出了一种改进的λ算法。该算法可以用于计算二维流动和轴对称流动。在导出了以广义黎曼变量表示的欧拉方程组后，本文用两步两点迎风格式对方程组离散求解。由于采用了广义黎曼变量表示的方程组，离散求解时充分考虑了变量的信息依赖域，所以算法稳定性好；由于仅用到待算点单侧一点的构造格式，所以算法简单，编程容易，同时也节省了计算时间。作为算例，我们对钝体超音绕流进行了广泛计算，结果表明，本算法速度快，稳定性好     

高阶精度CE/SE算法及其应用

对时-空守恒元解元算法(CE/SE)的网格设置做较大改进,提出一种新的六面体解元和元定义;同时在解元中对物理量进行高阶Taylor展开,给出一种在时间和空间上均具有高阶精度CE/SE算法.在此基础上,把新型的高阶精度CE/SE算法推广应用于高速流动捕捉激波间断、气相化学反应流动、计及固体动态效应的流体-弹塑性流动和非稳态多相不可压缩粘性流动中.数值实践表明,提出的新型网格结构上的高阶精度CE/SE算法具有算法简单、计算精度高、计算效率和计算效果好的优点,并大大改进和拓展了CE/SE算法的应用范围.     

求解Euler方程的空间—时间守恒格式

本文在CE／SE方法的基础上，提出了空间－时间守恒（STC）格式，其特点是构造简单，物理概念清晰，守恒性好，计算速度快且精度高，容易推广到多维流动及粘性流动。通过对二维Euler方程STC格式的介绍，可以看出这一方法的主要特点。与其它格式的计算结果或精确解相比较表明，用STC格式计算的结果是令人满意的。     

求解Navier-Stokes方程组的组合紧致迎风格式

给出一种新的至少有四阶精度的组合紧致迎风(CCU)格式,该格式有较高的逼近解率,利用该组合迎风格式,提出一种新的适合于在交错网格系统下求解Navier-Stokes方程组的高精度紧致差分投影算法.用组合紧致迎风格式离散对流项,粘性项、压力梯度项以及压力Poisson方程均采用四阶对称型紧致差分格式逼近,算法的整体精度不低于四阶.通过对Taylor涡列、对流占优扩散问题和双周期双剪切层流动问题的计算表明,该算法适合于对复杂流体流动问题的数值模拟.     

双相各向同性介质BISQ模型弹性波方程数值模拟方法

本文从Taylor级数展开式出发,推导出了交错网格一阶空间导数的任意偶数阶精度展开式和相应差分系数计算式;从本构方程和运动方程推导出了BISQ模型双相介质一阶双曲型应力-速度弹性波方程交错网格任意偶数阶精度差分格式以及推导出二维双相各向同性介质完全吸收层边界条件公式和相应的高阶交错网格差分格式。通过数值模拟研究表明,该方法边界吸收效果好,稳定性好,能够高精度模拟双相介质中地震弹性波场,且计算效率也高。     

对流项离散格式的对比与讨论

本文简单介绍了利用规正变量定义的各种对流项差分格式,给出了利用有限容积法离散粘性对流一扩散问题时的离散方程,其中的对流项采用高阶格式进行离散。以方腔顶盖驱动及圆管突扩区内层流流动考察了各种格式的计算精度与时效。通过对比分析得出:对于常规区域中的流动, QUICK、中心差分(CD)及SMART三种格式的精度与计算时效是比较合理的。     

流动变量线性分布的MUSCL格式

本文提出一种线性函数斜率的确定方法并证明用其近似代替网格内流动变量的初始分布,MUSCL格式具有二阶精度。引入单调性限制条件和一定的耗散机制后,该方法适合于Euler坐标系下的计算。本文在处理间断时,用激波关系式代替特征线方程,解决了特征线法在全流场计算中的应用问题。最后,本文给出Emery问题和一个火箭喷流问题的计算结果。     

求解稳恒磁场的谐函数展开法

推导出稳恒磁场矢势的谐函数展开式,当稳恒电流的分布适宜于用直角坐标系表示时,可应用该展开式求解磁场,给出了应用该展开式求解稳恒磁场的例子。     

二阶STC格式及其对跨音速湍流流动的数值模拟

ＳＴＣ格式是一种求解积分形式物理守恒律的计算方法,具有守恒性好,精度高的特点。目前求解Ｅｕｌｅｒ方程的ＳＴＣ格式已经建立起来,但求解Ｎ－Ｓ方程的ＳＴＣ格式尚在发展之中。为了使ＳＴＣ格式能够有效地求解粘性流动的问题,本文构造出了求解曲线坐标系下的二维Ｎ－Ｓ方程的二阶ＳＴＣ格式。用该格式对跨音速湍流流动问题进行了计算。     

QUICK格式在湍流旋流流动数值模拟中的应用

为研究不同精度的离散格式对湍流旋流流动数值模拟结果的影响,同时应用QUICK格式和混合格式对同轴射流旋流燃烧室内的湍流流动进行了数值模拟.在采用k-ε湍流模型的条件下,QUICK格式计算得到的燃烧室内气体轴向与切向速度及轴向脉动速度均方根值分布与实验数据符合较好,而混合格式给出的数值模拟结果则与实验有一定的偏差.     

Acoustic transmission in non-uniform ducts with mean flow,part II: The finite element method

This second paper in a two part series describes the implementation of the finite element method for the solution of the problem of acoustic transmission through a non-uniform duct carrying a high speed subsonic compressible flow. A finite element scheme based on both the Galerkin method and the residual least squares method and with eight noded isoparametric elements is described. Multi-modal propagation is investigated by coupling of the solution in the duct non-uniform section to modal expansions in uniform sections. The accuracy of the finite element results for both the eigenvalue and transmission problems is assessed by comparison with exact solutions and with results from the method of weighted residuals in the form of a modified Galerkin method as introduced in Part I of this pair of papers. The results of calculations show that modal interactions, particularly in transmitted modes, become increasingly important with increasing duct flow Mach number. Power transmission coefficient calculations for the geometries studied reveal no indication of a linear basis for the phenomenon of subsonic acoustic choking.     

用STC格式求解二维激波─边界层相互作用问题

将空间－时间守恒（ＳＴＣ）格式应用于求解Ｎ－Ｓ方程,并对激波－边界层相互作用问题进行了计算．结果表明,该方法可捕获激波与边界层相互作用的各种现象,显示了优良的数值模拟性能。     

用STC格式求解二维激波—边界层相互作用问题

将空间—时间守恒(STC)格式应用于求解N-S方程,并对激波—边界层相互作用问题进行了计算。结果表明,该方法可捕获激波与边界层相互作用的各种现象,显示了优良的数值模拟性能。     

An implementation of the exponential time differencing scheme to the magnetohydrodynamic equations in a spherical shell

Over the last decade there has been renewed interest in applying exponential time differencing (ETD) time stepping schemes to the solution of stiff systems. In this paper, we present an implementation of such a scheme to the fully spectral solution of the incompressible magnetohydrodynamic equations in a spherical shell. One problem associated with ETD schemes is the accurate calculation of the necessary matrices; we implement and discuss in detail a variety of different methods including direct computation, contour integration, spectral expansions and recurrence relations. We compare the accuracy of six different second-order methods in determining the evolution of a three-dimensional magnetic field under the action of a prescribed time-dependent flow of electrically conducting fluid, and find that for the timestep restriction imposed by the nonlinear terms, ETD methods are no more accurate than linearly implicit methods which have the significant advantage of being easier to implement. However, ETD methods are more readily extendable than those which are linearly implicit and will become much more advantageous at higher order.     

A unified gas-kinetic scheme for continuum and rarefied flows

With discretized particle velocity space, a multiscale unified gas-kinetic scheme for entire Knudsen number flows is constructed based on the BGK model. The current scheme couples closely the update of macroscopic conservative variables with the update of microscopic gas distribution function within a time step. In comparison with many existing kinetic schemes for the Boltzmann equation, the current method has no difficulty to get accurate Navier–Stokes (NS) solutions in the continuum flow regime with a time step being much larger than the particle collision time. At the same time, the rarefied flow solution, even in the free molecule limit, can be captured accurately. The unified scheme is an extension of the gas-kinetic BGK-NS scheme from the continuum flow to the rarefied regime with the discretization of particle velocity space. The success of the method is due to the un-splitting treatment of the particle transport and collision in the evaluation of local solution of the gas distribution function. For these methods which use operator splitting technique to solve the transport and collision separately, it is usually required that the time step is less than the particle collision time. This constraint basically makes these methods useless in the continuum flow regime, especially in the high Reynolds number flow simulations. Theoretically, once the physical process of particle transport and collision is modeled statistically by the kinetic Boltzmann equation, the transport and collision become continuous operators in space and time, and their numerical discretization should be done consistently. Due to its multiscale nature of the unified scheme, in the update of macroscopic flow variables, the corresponding heat flux can be modified according to any realistic Prandtl number. Subsequently, this modification effects the equilibrium state in the next time level and the update of microscopic distribution function. Therefore, instead of modifying the collision term of the BGK model, such as ES-BGK and BGK–Shakhov, the unified scheme can achieve the same goal on the numerical level directly. Many numerical tests will be used to validate the unified method.     

蛟路江河口海域污染分析及非线性扩散数值解

在分析蛟路江河口海域流态和污染规律的基础上,考虑盐淡水混合河口海域的污染非线性扩散现象,用有限元法进行数值分析计算,对数值解的稳定性进行了探讨,并将计算值与实测值进行了比较、验证.     

非结构网格下涡轮级三维非定常N-S方程的数值解

本文在非结构网格下,采用时间上二阶精度、空间上不低于二阶的高分辨率格式求解涡轮级三维流场,得到了与实验数据大体接近的N-S方程数值解。计算表明:本文所构造的双时间步迭代格式具有稳定、高效的特征。实践显示:本文用FORTRAN与C语言混合编制的N-S方程源程序,可用于涡轮级三维非定常流场计算。     

Embedding sharp interfaces within the lattice Boltzmann method for fluids with arbitrary density ratios

Current lattice Boltzmann methods for simulating two fluids create a diffuse interface between the fluids. In this work, we develop a novel technique for embedding sharp interfaces between fluids with unbounded density ratios for the LB method. Distribution functions streamed across an interface are transformed so that the receiving node is passed information corresponding to its fluid phase. Two different methods are employed to determine the transformation. The first uses analytical distribution functions from steady Poiseuille flow to determine the jump in moments of the distribution functions across the interface. The second uses approximate expansions of distribution functions to determine jumps in distribution functions. The accuracy and stability of the methods are examined in simulations of Poiseuille-Couette flows with an interface parallel to the walls. Both methods show linear convergence to the analytical solution.     

An element-free Galerkin(EFG) method for numerical solution of the coupled Schrdinger-KdV equations

The present paper deals with the numerical solution of the coupled Schrdinger-KdV equations using the elementfree Galerkin(EFG) method which is based on the moving least-square approximation.Instead of traditional mesh oriented methods such as the finite difference method(FDM) and the finite element method(FEM),this method needs only scattered nodes in the domain.For this scheme,a variational method is used to obtain discrete equations and the essential boundary conditions are enforced by the penalty method.In numerical experiments,the results are presented and compared with the findings of the finite element method,the radial basis functions method,and an analytical solution to confirm the good accuracy of the presented scheme.