PCCSAP-3D程序压力场算法改进

介绍大型先进压水堆安全壳专用分析程序PCCSAP-3D计算采用的方法,引入GMRES(Generalized Minimal RESidual)方法改进该程序的压力场算法.使用GMRES算法的实用变形,并采用合适的预处理技术,比较GMRES算法和ML-ADI算法在求解压力方程时的收敛速度.结果表明,利用压力矩阵结构化和稀疏性的特点,采用预处理GMRES算法能够更快速地求解压力方程.当压力矩阵规模变大时,GMRES算法相对于ML-ADI方法能够节省更多的时间.     

网格单元形状对数值计算的影响

实现了二维非结构化网格上的N-S方程的离散,编制了非结构化同位网格上的SIMPLE程序,针对CFD/NHT 中几个有基准解的问题进行了试算考核。结果表明,在步长基本相同的情况下,四边形网格的收敛速度和解的精度都优于 三角形网格,尤其是收敛速度更明显;使用考虑边界贴体特性的边界层网格,解的精度优于均匀网格。     

一种可压缩流动的高阶加权紧致非线性格式(WCNS)的加速收敛方法

以高超声速粘性绕流的数值模拟为例,研究LU-SGS、高斯-赛德尔点松弛、线松弛以及GMRES等隐式求解方法在空间项采用高阶精度格式WCNS离散时的收敛性,并对GMRES(generalized minimal residual)方法中的子迭代影响作了对比计算.结果表明,采用准确的解析雅克比矩阵的点、线松弛的收敛速度优于LU-SGS,以线松弛为预处理的GMRES算法具有良好的收敛特性.     

GMRES算法在二维定常无粘流计算中的应用

发展了GMRES算法的两种不同预处理方法求解二维无粘流体动力学方程组。在保证计算效率的基础上,采用了一种减小内存需求的途径。用两个算例对GMRES算法以及两种不同的预处理方法进行分析,同时与DDADI方法进行比较。通过对NACA0012有攻角超临界流动以及GAMM通道超音流的计算,表明两种预处理下的GMRES算法都具有收敛速度快的优点,LUSGS预处理方法略优于ILU预处理方法。     

简谐势阱中中性原子非线性薛定谔方程的定态解

给出了非线性定态薛定谔方程(NLSE)数值求解的一般方法,并求解了简谐势阱中中性原子NLSE的基态和激发态解．讨论了NLSE的波函数收敛与归一化问题,并对计算精度进行了分析. 关键词：     

大分离条件下风力机叶片三维定常数值模拟研究

为了改善失速条件下风力机气动特性的CFD模拟精度,采用定常的RANS求解方法和一方程S-A湍流模型,数值模拟定桨距型风轮叶片LM19在高风速(18m/s)条件下的气动特性.首先讨论了由流动大尺度分离导致计算收敛曲线大幅度振荡时数值结果的处理方法,然后分析了计算域尺度和网格密度对数值模拟结果的影响,为失速条件下风力机气动...     

基于局部加密纯无网格法非线性Cahn-Hilliard方程的模拟

为数值求解描述不同物质间相位分离现象的高阶非线性Cahn-Hilliard(C-H)方程,发展了一种基于局部加密纯无网格有限点集法(local refinement finite pointset method,LR-FPM).其构造过程为:1)将C-H方程中四阶导数降阶为两个二阶导数,连续应用基于Taylor展开和加权最小二乘法的FPM离散空间导数;2)对区域进行局部加密和采用五次样条核函数以提高数值精度;3)局部线性方程组求解中准确施加含高阶导数Neumann边值条件.随后,运用LR-FPM求解有解析解的一维/二维C-H方程,分析粒子均匀分布/非均匀分布以及局部粒子加密情况的误差和收敛阶,展示了LR-FPM较网格类算法在非均匀布点情况下的优点.最后,采用LR-FPM对无解析解的一维/二维C-H方程进行了数值预测,并与有限差分结果相比较.数值结果表明,LR-FPM方法具有较高的数值精度和收敛阶,比有限差分法更易数值实现,能够准确展现不同类型材料间相位分离非线性扩散现象随时间的演化过程.     

非线性薛定谔方程的高阶分裂改进光滑粒子动力学算法

为提高传统光滑粒子动力学(SPH)方法求解高维非线性薛定谔(nonlinear Schr?dinger/Gross-Pitaevskii equation, NLS/GP)方程的数值精度和计算效率,本文首先基于高阶时间分裂思想将非线性薛定谔方程分解成线性导数项和非线性项,其次拓展一阶对称SPH方法对复数域上线性导数部分进行显式求解,最后引入MPI并行技术,结合边界施加虚粒子方法给出一种能够准确、高效地求解高维NLS/GP方程的高阶分裂修正并行SPH方法.数值模拟中,首先对带有周期性和Dirichlet边界条件的NLS方程进行求解,并与解析解做对比,准确地得到了周期边界下孤立波的奇异性,且对提出方法的数值精度、收敛速度和计算效率进行了分析;随后,运用给出的高阶分裂粒子方法对复杂二维和三维NLS/GP问题进行了数值预测,并与其他数值结果进行比较,准确地展现了非线性孤立波传播中的奇异现象和玻色-爱因斯坦凝聚态中带外旋转项的量子涡旋变化过程.     

用代数多重网格法求解一维分裂格式的Euler方程

提出了代数多重网格法(AMG)的一种新算法。新算法改进了插值公式和粗网格方程,并把它应用到求解一维的分裂格式Euler方程。数值结果表明,对于具有高CFL条件数的Euler方程,代数多重网格法可以求解;对于Gaus-Seidel方法求解不能收敛的代数方程组,代数多重网格法求解可以收敛。新算法改进了代数多重网格法的收敛性和扩展了它的应用范围,数值结果表明了它的有效性和强壮性。     

自旋为5/2的Bargmann-Wigner方程的严格解

在坐标表象中严格求解自旋为5/2的Bargmann-Wigner方程,导出了自旋为5/2的场(m≠0)的相对论性方程和动量表象波函数 关键词： 自旋为5/2的场(m≠0) Bargmann-Wigner方程 坐标表象 严格解     

Preconditioning methods for discontinuous Galerkin solutions of the Navier–Stokes equations

A Newton–Krylov method is developed for the solution of the steady compressible Navier–Stokes equations using a discontinuous Galerkin (DG) discretization on unstructured meshes. Steady-state solutions are obtained using a Newton–Krylov approach where the linear system at each iteration is solved using a restarted GMRES algorithm. Several different preconditioners are examined to achieve fast convergence of the GMRES algorithm. An element Line-Jacobi preconditioner is presented which solves a block-tridiagonal system along lines of maximum coupling in the flow. An incomplete block-LU factorization (Block-ILU(0)) is also presented as a preconditioner, where the factorization is performed using a reordering of elements based upon the lines of maximum coupling. This reordering is shown to be superior to standard reordering techniques (Nested Dissection, One-way Dissection, Quotient Minimum Degree, Reverse Cuthill–Mckee) especially for viscous test cases. The Block-ILU(0) factorization is performed in-place and an algorithm is presented for the application of the linearization which reduces both the memory and CPU time over the traditional dual matrix storage format. Additionally, a linear p-multigrid preconditioner is also considered, where Block-Jacobi, Line-Jacobi and Block-ILU(0) are used as smoothers. The linear multigrid preconditioner is shown to significantly improve convergence in term of number of iterations and CPU time compared to a single-level Block-Jacobi or Line-Jacobi preconditioner. Similarly the linear multigrid preconditioner with Block-ILU smoothing is shown to reduce the number of linear iterations to achieve convergence over a single-level Block-ILU(0) preconditioner, though no appreciable improvement in CPU time is shown.     

Improvement for optical mechanics method of coherent gradient sensing

Coherent gradient sensing (CGS) is double grating lateral-shearing interferometric technique with the simplicity of the optical set-up, non-contact, real-time, full-field optical information and variable resolution, which has shown many applications in the study of quasi-static as well as dynamic crack-tip field in both homogeneous and composite materials. It can be used both in a reflection mode (for opaque materials) and in a transmission mode (for transparent materials). The accuracy of the fringe order in the CGS interference image will deeply influence the precision of experimental study. Because of the difference in the optical principle from other optical methods, the fringe order of CGS cannot be obtained through the phase-shift technology. In this paper, a kind of modified CGS method is introduced and analyzed, which can accurately obtain the fringe order of random position in the CGS interference image. This method does not need additional optical set-up and complicated image processing techniques, but only needs several (greater than two) CGS interference images under different loadings. Static fracture experiments show that this method can evidently improve the precision of the CGS method.     

"New-version-fast-multipole-method" accelerated electrostatic interactions in biomolecular systems

In this paper, we present an efficient and accurate numerical algorithm for calculating the electrostatic interactions in biomolecular systems. In our scheme, a boundary integral equation (BIE) approach is applied to discretize the linearized Poisson-Boltzmann (PB) equation. The resulting integral formulas are well conditioned for single molecule cases as well as for systems with more than one macromolecule, and are solved efficiently using Krylov subspace based iterative methods such as generalized minimal residual (GMRES) or bi-conjugate gradients stabilized (BiCGStab) methods. In each iteration, the convolution type matrix-vector multiplications are accelerated by a new version of the fast multipole method (FMM). The implemented algorithm is asymptotically optimal O(N) both in CPU time and memory usage with optimized prefactors. Our approach enhances the present computational ability to treat electrostatics of large scale systems in protein-protein interactions and nano particle assembly processes. Applications including calculating the electrostatics of the nicotinic acetylcholine receptor (nAChR) and interactions between protein Sso7d and DNA are presented.     

高功率半导体激光器微通道热沉的方案设计

 对用于高功率半导体激光器的叠片式微通道热沉进行方案设计,利用计算流体力学和数值传热学对各种方案进行数值仿真,研究了微通道的特征尺寸和流量等因素对冷却效果和流动阻力特性的影响,一般情况下,减小微通道的特征尺寸和增加冷却水的流量可以降低传热热阻,但增加了流动压力损失;另外对金刚石热扩散片（次热沉）的效果也进行了数值计算,计算结果表明:金刚石热扩散片在该类型问题中降低温度作用明显。     

基于非线性涡格法的快速静气动弹性数值模拟技术

基于2.5D RANS数据和VLM耦合的方式,发展了一种考虑非线性流动效应的混合型涡格法HVLM.采用矩形直/后掠机翼两个外形的跨声速算例,通过与VLM、三维CFD计算数据的比较,对HVLM的气动力预测精度进行了分析与评估.对比结果表明,HVLM在大幅降低时间成本的前提下可以获得和三维CFD方法预测值十分接近的计算数据,对线化VLM方法的修正效果显著.然后,HVLM与悬臂梁有限元求解耦合,实现了一种面向三维机翼的快速静气动弹性数值模拟技术,并通过矩形直机翼算例进行了验证.耦合算例的时间分析数据表明,HVLM/Beam耦合的方式能够在10 s以内完成1次三维机翼静气动弹性分析,在气动/结构耦合分析、优化设计方面展示出了良好的应用前景.      

小型轴流CPU风扇的CFD分析

轴流风扇被广泛应用于CPU的热管理中,作为散热关键部件,其运行状态是否良好直接影响计算机的散热性能和寿命.本文利用NUMECA的FINE~(TM)/Turbo软件包对两个小型轴流CPU风扇内部流动进行了详细的数值模拟,并与AMCA风洞的试验测试结果进行了验证对比,在此基础上对小型轴流CPU风扇内部流场进行了详细的分析,并探讨了如何提高这类风扇性能数值预测精度的途径.     

Computation of linear and nonlinear stationary states of photonic structures using modern iterative solvers

In this paper we describe efficient methods to obtain the stationary states of linear and nonlinear photonic systems, which have gained particular interest in the field of integrated and nonlinear optics. While the methods presented are directly applicable to optical physics, they are also general and should be of interest in a broad range of phenomena presently under study in other areas of physics and engineering. The strategy consists in combining the use of classical methods, such as inverse iteration or the Newton method, together with modern, nonstationary linear solvers, such as SYMMLQ or GMRES, in order to obtain efficient numerical computations to problems involving large matrices. We have selected several example problems in order to discuss the practical implementation details, not normally described in the present literature. Moreover, the problems we have selected provide a backdrop to contrast and motivate the use of different methods for systems which are symmetric and non-symmetric, single and multi-component, and also real and complex. Information relative to numerical performance of the different algorithms, including a survey for a nonsymmetric problem, which requires the adjustment of a restarting parameter for the GMRES algorithm, is also presented.     

JFNK方法在S N输运计算中的应用

JFNK(Jacobian-free Newton-Krylov)方法是一种求解非线性方程的高效迭代算法.传统输运计算中的负通量修正与k-特征值迭代使得原本线性的输运计算转变为非线性问题数值求解.为提高非线性输运问题的计算效率,将这两类非线性问题离散成残差形式的非线性方程组,并采用JFNK方法对其进行迭代求解.分析不同...     

A dispersion minimizing finite difference scheme and preconditioned solver for the 3D Helmholtz equation

In this paper, a new 27-point finite difference method is presented for solving the 3D Helmholtz equation with perfectly matched layer (PML), which is a second order scheme and pointwise consistent with the equation. An error analysis is made between the numerical wavenumber and the exact wavenumber, and a refined choice strategy based on minimizing the numerical dispersion is proposed for choosing weight parameters. A full-coarsening multigrid-based preconditioned Bi-CGSTAB method is developed for solving the linear system stemming from the Helmholtz equation with PML by the finite difference scheme. The shifted-Laplacian is extended to precondition the 3D Helmholtz equation, and a spectral analysis is given. The discrete preconditioned system is solved by the Bi-CGSTAB method, with a multigrid method used to invert the preconditioner approximately. Full-coarsening multigrid is employed, and a new matrix-based prolongation operator is constructed accordingly. Numerical results are presented to demonstrate the efficiency of both the new 27-point finite difference scheme with refined parameters, and the preconditioned Bi-CGSTAB method with the 3D full-coarsening multigrid.     

Numerical analyses of radiative heat transfer in any arbitrarily-shaped axisymmetric enclosures

A numerical approach for the treatment of radiative heat transfer in any irregularly-shaped axisymmetric enclosure filled with absorbing, emitting and scattering gray media is developed. Radiative transfer equation (RTE) is formulated for a general axisymmetric geometrical configurations, and the discretized equation is conducted using an unstructured meshes, generated by an appropriate computer algorithm, and the control volume finite element method which frequently adopted in CFD problems. A computer procedure has been done to solve the discretized RTE and to examine the accuracy and the computational efficiency of the proposed numerical approach. By using this computer algorithm, five test cases, a cylindrical enclosure with absorbing and emitting medium, a diffuser shaped axisymmetric enclosure, a finite axisymmetric cylindrical enclosure with a curved wall, a furnace with axially varying medium temperature and a rocket nozzle, are treated and the obtained results agree very well with other published works. Furthermore, the developed computer procedure has an accurate CPU time and it can be coupled easily with CFD codes.