非静力模式GRAPES的预条件技术研究

GRAPES是中国气象科学研究院研制的一个非静力格点模式,该模式以大气运动的全可压运动方程为基础,采用半隐半Lagrange方案。在模式积分中,每个时间步需要求解关于气压梯度力的三维离散Helmholtz方程,该方程组的求解在整个数值模拟时间中占70%左右,为加速求解过程,采用高效预条件技术是必然选择。将提出的多行双门槛不完全分解预条件与国内外常用的多种其他预条件技术进行了比较,同时,考查了针对不完全分解预条件的加性Schwarz与基于因子组合的两种并行化预条件技术,结果发现,多行双门槛不完全分解预条件优于包括ILUT在内的其他不完全分解预条件,且加性Schwarz略优于基于因子组合的并行预条件技术。     

一种解抛物型方程的三层九点高精度加权差分格式

针对一维齐次常系数抛物型方程,采用显隐格式加权,构造出一种在时间和空间上分别达到四阶和八阶的高精度差分格式,通过理论推导,给出了满足稳定性条件的网比取值范围.通过数值实验及与文献方法的对比,验证了本文格式在满足稳定性的基础上可以达到预期的理论精度.     

数值天气预报全球谱模式并行计算研究

本文首先给出数值天气预报全球谱模式的控制方程;接着,利用数值天气预报全球谱模式计算的复杂性和数据整体相关性,给出了基于二维数据剖分方法的并行算法,并从负载平衡、减少通信延迟以及Cache与I／O优化三个方面给出了并行实现策略。     

随机外激非线性系统FPK方程的四阶中心C-N型隐式差分解

研究了非线性随机动力系统所对应的Fokker-Planck-kolmogorov(FPK)方程.讨论了微分方程的可朗克(Crank)一尼考尔逊(Nicolson)型隐式有限差分格式以及微分的四阶中心差分格式,将两者相结合,得到FPK方程的四阶中心C-N隐式格式差分解,并与FPK方程的精确解进行了比较.数值结果表明,该方...     

全球谱模式T213L31在PC机群系统上的并行实现

本文研究以PC作为结点的Linux机群系统上实现全球谱模式T213L31并行计算的方法,给出了谱模式的三维置换并行算法和半拉格朗日时间积分格式的按需通讯并行实现方法,同时提出了适合于机群系统的并行I/O实现。该实现在由四个双CPU结点组成的Linux机群环境下取得了良好的运行效果。     

非理想条件下CCM模式Boost变换器的分析

本文以工作于电流连续模式下的Boost型变换器为例,根据能量守恒原理并用三端开关器件模型法建立了考虑电路元件的寄生效应以及开关元件的非理想开关特性时的大信号平均模型、DC和小信号电路模型.对寄生参数的存在给系统性能带来的影响进行了理论分析和仿真实验,分析与实验结果对进一步优化Boost型变换器性能具有很高的参考价值.     

二维非结构网格浅水波方程的二阶精度非振荡有限体积方法

考虑浅水波方程,对二维非结构网格给出了一种非振荡有限体积方法.该方法的主要思想是在每一个三角形单元上采用最小二乘的思想构造一个重构函数,而时间离散采用二步TVD Runge- Kutta方法.最后用该格式对二维溃坝问题进行了数值试验,得到了满意的结果.     

An optimal compact sixth-order finite difference scheme for the Helmholtz equation

In this paper, we present an optimal compact finite difference scheme for solving the 2D Helmholtz equation. A convergence analysis is given to show that the scheme is sixth-order in accuracy. Based on minimizing the numerical dispersion, a refined optimization rule for choosing the scheme’s weight parameters is proposed. Numerical results are presented to demonstrate the efficiency and accuracy of the compact finite difference scheme with refined parameters.     

A high-order compact scheme for the one-dimensional Helmholtz equation with a discontinuous coefficient

In this paper, based on the idea of the immersed interface method, a fourth-order compact finite difference scheme is proposed for solving one-dimensional Helmholtz equation with discontinuous coefficient, jump conditions are given at the interface. The Dirichlet boundary condition and the Neumann boundary condition are considered. The Neumann boundary condition is treated with a fourth-order scheme. Numerical experiments are included to confirm the accuracy and efficiency of the proposed method.     

Note on a Fourth Order Finite Difference Scheme for the Wave Equation

The linear wave equation is one of the simplest partial differential equations. It has been used as a test equation of hyperbolic systems for different numerical schemes [Richtmyer and Morton (1967); Euvrard (1994); and Lax (1990]. In this short note, a Fourth order finite difference scheme for this equation is proposed and studied. Numerical simulations confirm our theoretical analyses of accuracy and stability condition. It will be interesting to extend the scheme to nonlinear hyperbolic systems.     

Multi-loop nonlinear internal model controller design under nonlinear dynamic PLS framework using ARX-neural network model

In this paper, a novel multi-loop nonlinear internal model control (IMC) strategy for multiple-input multiple-output (MIMO) systems is presented under the partial least squares (PLS) framework, which automatically decomposes the system into several univariate subsystems in the latent space. To formulate a nonlinear dynamic PLS framework, we propose an ARX-neural network (ARX-NN) cascaded structure, and incorporate it into PLS inner model. A gradient-based optimization approach is then provided to identify the parameter sets of the ARX-NN PLS model so that the plant-model mismatch is minimized. Furthermore, with perfect model, we show that the response of the closed loop system can be reduced to a simple linear IMC filter with the original system delay. The simulation results of a methylcyclohexane (MCH) distillation column from Aspen Dynamic Module, demonstrate the effectiveness of our approach in terms of disturbance rejection and tracking performance.     

广义Maxwell流体分数阶微分方程的数值解法

针对广义Maxwell粘弹性流体分数阶微分方程,建立了一种隐式差分格式,给出了数值解的求解公式,证明了隐式差分格式稳定性与收敛性。     

A linearized implicit finite-difference method for solving the equal width wave equation

A linearized implicit finite-difference method is presented to find numerical solutions of the equal width wave equation. The method has been used successfully to investigate the motion of a single solitary wave, the development of the interaction of two solitary waves and an undular bore. The obtained results are compared with other numerical results in the literature. A stability analysis of the scheme is also investigated.     

A high-order ADI scheme for the two-dimensional time fractional diffusion-wave equation

In this paper, a compact alternating direction implicit finite difference scheme for the two-dimensional time fractional diffusion-wave equation is developed, with temporal and spatial accuracy order equal to two and four, respectively. The second-order accuracy in the time direction has not been achieved in previous studies.     

A CCD-ADI method for two-dimensional linear and nonlinear hyperbolic telegraph equations with variable coefficients

In this paper, a combined compact finite difference method (CCD) together with alternating direction implicit (ADI) scheme is developed for two-dimensional linear and nonlinear hyperbolic telegraph equations with variable coefficients. The proposed CCD-ADI method is second-order accurate in time variable and sixth-order accurate in space variable. For the linear hyperbolic equation, the CCD-ADI method is shown to be unconditionally stable by using the Von Neumann stability analysis. Numerical results for both linear and nonlinear hyperbolic equations are presented to illustrate the high accuracy of the proposed method.     

复杂圆柱壳结构参数化建模方法及模型库设计

针对船舶的主要结构形式——复杂圆柱壳结构,为研究其快速建模方法以实现船舶结构的优化设计,基于隐式参数化模型概念提出参数化模型表征方法,建立其分类和命名体系,给出其参数化建模方式和流程,利用数值仿真工具完成其参数化模型库设计和开发,并应用于某船舶结构的快速建模.算例表明:复杂圆柱壳参数化模型库设计合理,满足复杂圆柱壳结构快速建模和修改的要求.