两同心旋转球间流动的数值模拟

利用Legendre和伴随Legendre函数来数值模拟定常和不定常的轴对称的同心旋转球间的不可压缩流体的流动.     

两个同心旋转球间的对称Taylor涡流

用有限元方法对两个同心旋转球间的稳态对称不可压流进行数值模拟,结果显示了超临界雷诺数下的三种流动模式:0-涡模式,1-涡模式和2-涡模式。     

用谱方法数值模拟槽道内的气固两相流动

在数值模拟领域内,谱方法具有收敛快、分辨率高和精度高的优点．谱方法处理边界方便,随着数值方法的改善和计算机的发展,它在数值模拟中的作用愈加重要．这里采用谱方法数值求解三维Ｎ—Ｓ方程,用这一方法计算了直槽道内流体的流动．计算得到的层流和湍流结果与理论结果符合地较好．在此基础之上进一步模拟了几种不同槽道内的三维粘性流体层流流动,特别在弯曲槽道内的流动计算中,发展了源项处理方法,正确地反映了弯曲固壁对流体流动的影响．通过对湍流计算获得的脉动速度场的统计可以得到湍流运动的许多统计量,正确地反映了湍流运动的特征,说明可以用模拟得到的流场来代替真实的流场．进行了气固两相流动的研究,由直接模拟得到的流体瞬时速度场对固体粒子的作用进行了粒子运动的模拟计算,得到了颗粒在真实流场中运动的浓度,轨道等有用信息和运动特性,得到了令人鼓舞的结果．     

谱元方法求解正方形封闭空腔内的自然对流换热

提出谱元方法计算正方形截面封闭空腔内的自然对流问题,具体求解了原始变量速度和压力的不可压Navier-Stokes方程和温度方程,所有的求为量均采用Chebyshev谱逼近,Navier-Stokes方程和温度方程的时间离散采用时间分裂法,非线性项用4阶Runge-Kutta法,扩散项用Crank-Nicolson半隐方法,获得了与文献发表的基准解较一致的计算结果。     

五维对流模式吸引子的Lyapunov谱

利用Lyapunov谱的算法,计算了五维对流非线性动力系统吸引子的Lyapunov谱及奇怪吸引子的维数。     

两种电磁场谱间断元方法的比较

时域间断元方法是近年来电磁场计算领域的重要进展之一。将基函数的插值点和数值积分点重合的质量集中技术是降低该间断元方法质量矩阵存储开销和提高计算效率的重要手段。通过谐振腔、带通滤波器以及光子晶体内的电磁场等数值算例,在四边形网格上比较了传统的质量集中算法和近来提出的Weight-Adjust算法之间的差异。计算结果表明,尽管两种方法的存储量一样,但Weight-Adjust算法具有更高的精度。     

一个新的恒Lyapunov指数谱混沌吸引子与电路实现

通过对改进恒Lyapunov指数谱混沌系统进行进一步演变,并引入新的绝对值项,发现了一种新的混沌吸引子.首先,通过相图、Poincar映射、Lyapunov指数以及功率谱,证明该混沌吸引子的存在性.接着,分析研究了这种新型混沌吸引子的基本动力学行为.Lyapunov指数谱、分岔图和状态变量幅值演变的数值仿真说明,该系统存在全局线性调幅参数,在该参数的调整下,系统输出三维信号的幅度皆能得到线性调整,而系统保持相同的混沌吸引子与Lyapunov指数谱.最后,通过构建电路实现了该混沌系统,观察到相应的混沌吸引子,也验证了全局线性调幅参数的调幅作用,数值仿真与电路实现有很好的一致性.     

数值模拟两相汽蚀流动的新模型和算法

提出了数值模拟两相汽蚀流动现象的新汽蚀模型和算法.提出的汽蚀模型和算法耦合了考虑紊流粘性效应的Reynolds-Averaged Navier-Stokes方程求解方法,可以自动模拟空泡起始点、空泡长度和汽蚀空泡形状.在流场计算和界面修正的迭代计算过程中,跟踪并得到液相/气相界面.数值模拟了圆锥形圆柱体和半球形圆柱体在不同汽蚀系数下的汽蚀流动现象,得到了与实验值完全吻合的数值模拟结果,并且与已发表的数值研究结果进行了比较.计算结果表明提出的汽蚀模型和算法能够有效地模拟汽蚀流动中的气泡界面和气泡长度,汽蚀模型和算法的正确性和实用性得到了相应的验证.     

混沌吸引子在两个周期振子耦合下的相同步

在分析了系统稳定的基础上，对非线性混沌吸引子在两个独立外周期振子耦合下的相同步进 行了研究.与一个周期振子耦合的情况不同，两个周期振子对混沌吸引子的耦合具有排他性 和竞争性，相同步在两个亚稳态交替出现，各自同步时间长度由外振子参数决定.确定了周 期外振子参数与同步时间长度的关系并与数值模拟计算结果进行了比较. 关键词： 混沌吸引子 相同步     

Radiative heat transfer to chemically reacting flow between concentric rotating spheres

Summary The hydromagnetic flow between two hot concentric rotating spheres in the presence of a chemical reaction is used to model the depletion of ozone by nitrogen and chlorine compounds in the middle atmosphere. It is observed that a 6% depletion of the ozone budget is easily plausible by the emission of anthropogenic material.

---

Riassunto Si usa il flusso idromagnetico tra due sfere concentriche calde e rotanti in presenza di una reazione chimica come modello dell'impoverimento di ozono carico di composti di azoto e di cloro nella media atmosfera. Si osserva che una riduzione del 6% del bilancio di ozono è facilmente spiegata dall'emissione di materiale antropogenico.

---

Резюме Для моделирования обеднения озона из-за соединений азота и хлора в средней атмосфере исследуется гидромагнитный поток между двумя нагретыми концентрическими вращающимися сферами в присутствии химических реакций. Отмечается, что 6% обеднение бюджета озона может быть обьясненио эмиссией антропогенных материалов.

     

Visualization of sudden-start flow between two concentric rotating cylinders with finite length

Numerical simulation and visualization are performed to investigate the developing processes of flows between two concentric rotating cylinders. The length of the cylinders is finite and the end walls are fixed. Initially the fluid is at rest, and the inner cylinder suddenly begins to rotate. Various flow modes appear in this flow. Developments of the flow to these modes are examined and the physical explanation for the transient process is presented. The processes are classified into some types. At low Reynolds numbers, vortices begin to grow on end walls. When the Reynolds number is higher, the centrifugal instability brings first vortices around the mid-plane in the axial direction. Some final modes are established via an intermediate mode, and some other modes are attained after merging and vanishing of vortices.     

Runge-Kutta间断Galerkin法在求解Navier-Stokes方程中的应用

Cockburn & Shu^[1] 在1988年提出了一种TVB Runge-Kuta局部投影的间断Galerkin有限元方法应用于Euler方程的求解,并取得了成功。文章将该方法进一步应用到Navier-Stokes方程的求解。     

A theoretical study of radiation between two concentric spheres using a modified discrete ordinates method associated with Legendre transform

A modified discrete ordinates method (DOM) is used in spherical participating media. The radiative intensity is broken up into two components. One component is traced back to the enclosure's source. It is called direct intensity. The other component is rather traced back to the contribution of the medium itself. It is called diffuse intensity. Thus, the radiative transfer equation (RTE) is transformed into two simultaneous equations: a direct RTE and a diffuse RTE. The direct RTE is solved analytically. The diffuse RTE is solved numerically using the DOM. The streaming angular derivative term appearing in spherical geometry is modeled by making use of the Finite Legendre Transform. We study a pure radiation transfer problem between two concentric spheres. The medium is assumed to be gray and isotropically scattering. The limiting spheres are considered to be opaque, gray, diffusely emitting and diffusely reflecting with uniform emissivity over each surface. The obtained results are compared with available cases reported in the literature. In particular, relative importance of the direct radiation in optically thin media is studied.     

Some Similarity Reduction Solutions to Two-Dimensional Incompressible Navier-Stokes Equation

We investigate the symmetry reduction for the two-dimensional incompressible Navier Stokes equation in conventional stream function form through Lie symmetry method and construct some similarity reduction solutions. Two special cases in [D.K. Ludlow, P.A. Clarkson, and A.P. Bassom, Stud. Appl. Math. 103 （1999） 183] and a theorem in [S.Y. Lou, M. Jia, X.Y. Tang, and F. Huang, Phys. Rev. E 75 （2007） 056318] are retrieved.     

Spectral element method for vector radiative transfer equation

A spectral element method (SEM) is developed to solve polarized radiative transfer in multidimensional participating medium. The angular discretization is based on the discrete-ordinates approach, and the spatial discretization is conducted by spectral element approach. Chebyshev polynomial is used to build basis function on each element. Four various test problems are taken as examples to verify the performance of the SEM. The effectiveness of the SEM is demonstrated. The h and the p convergence characteristics of the SEM are studied. The convergence rate of p-refinement follows the exponential decay trend and is superior to that of h-refinement. The accuracy and efficiency of the higher order approximation in the SEM is well demonstrated for the solution of the VRTE. The predicted angular distribution of brightness temperature and Stokes vector by the SEM agree very well with the benchmark solutions in references. Numerical results show that the SEM is accurate, flexible and effective to solve multidimensional polarized radiative transfer problems.     

Radiative heat transfer between two concentric spheres separated by a two-phase mixture of non-gray gas and particles using the modified discrete-ordinates method

The radiative heat transfer between two concentric spheres separated by a two-phase mixture of non-gray gas and a cloud of particles is investigated by using the combined finite-volume and discrete-ordinates method, named modified discrete-ordinates method (MDOM), which integrates the radiative transfer equation (RTE) over a control volume and a control angle simultaneously like in the finite-volume method (FVM) and treats the angular derivative terms due to spherical geometry as the conventional discrete-ordinates method (DOM). The radiative properties involving non-gray gas and particle behavior are modeled by using the extended weighted sum of gray gases model (WSGGM) with particles. Mathematical formulation and final discretization equations for the RTE are introduced by considering the behavior of a two-phase mixture of non-gray gas and particles in a spherically symmetric concentric enclosure. The present approach is validated by comparing with the results of previous works including gray and non-gray radiative heat transfer. Finally, a detailed investigation of the radiative heat transfer with non-gray gases and/or a two-phase mixture is conducted to examine the dependence of the radiative heat transfer upon temperature ratio between inner and outer spherical enclosure, particle concentration, and particle temperature.     

A semi-implicit lattice method for simulating flow

We propose a new semi-implicit lattice numerical method for modeling fluid flow that depends only on local primitive variable information (density, pressure, velocity) and not on relaxed upstream distribution function values. This method has the potential for reducing parallel processor communication and permitting larger time steps than the lattice-Boltzmann method. Several benchmark problems are solved to demonstrate the accuracy of the method.     

Spectral Element Discretization of the Stokes Equations in Deformed Axisymmetric Geometries

In this paper, we study the numerical solution of the Stokes system in deformed axisymmetric geometries. In the azimuthal direction the discretization is carried out by using truncated Fourier series, thus reducing the dimension of the problem. The resulting two-dimensional problems are discretized using the spectral element method which is based on the variational formulation in primitive variables. The meridian domain is subdivided into elements, in each of which the solution is approximated by truncated polynomial series. The results of numerical experiments for several geometries are presented.