New solitary wave solutions of (2+1)-dimensional space–time fractional Burgers equation and Korteweg–de Vries equation

In this article, via the improved fractional subequation method, the fully analytical solutions of the (2+1)-dimensional space–time fractional Burgers equation and Korteweg–de Vries equation involving Jumarie’s modified Riemann–Liouville derivative have been derived. As a result, with the aid of symbolic computation, many types of new analytical solutions are obtained, which include new solitary wave, periodic wave and rational wave solutions. The graphical representations show that these gained solutions have abundant structures.     

0.85THz可调谐式折叠波导再生反馈真空电子学振荡器的理论及实验研究

本文提出了一种适用于850 GHz太赫兹波成像系统的可调谐再生反馈振荡器。使用UV-LIGA微加工工艺制作慢波结构,可满足折叠波导在太赫兹频段的尺寸需求。使用CST微波工作室对折叠波导色散特性进行设计,同时针对于行波管和再生反馈振荡器中折叠波导的结构,阐明了影响频率调谐的因素。此外,对带衰减的反馈回路进行仿真模拟,并使用三维粒子模拟验证了整体设计。改变电子注电压可实现振荡频率可调,振荡从单频状态逐渐变为多频状态,整体输出功率均大于200 mW。     

基于近似黎曼求解器的三维浅水方程组求解方法

将求解平面二维浅水方程组的Godunov型有限体积法扩展至求解三维浅水方程组,建立具有激波捕捉特性的三维数学模型,将扩大三维浅水方程数学模型的应用范围。模型中湍流封闭采用非线性K-ε模型,水平方向数值通量采用HLLC近似黎曼求解器计算。为改善数值格式稳定性,垂向扩散项采用隐式离散,且在局部小水深处将三维模型退化为水深平均平面二维模型,所开发的模型在形式上具有时、空二阶精度。随后采用水跃、干河床溃坝洪水演进等算例对模型进行检验,结果表明:该模型具有较好的稳定性,能保证静水平衡,在间断解处能给出高分辨率的数值解,并具有较好的干湿边界模拟能力。     

基于有限体积法Godunov格式的水锤计算模型

针对管道内水锤问题,基于一阶和二阶Godunov格式的有限体积法建立数学模型并进行模拟分析。采用Riemann求解器对离散通量进行求解,同时在计算中引入对流项;采用MUSCL-Hancock方法进行重构得到二阶精度的Godunov格式,为了避免虚假振荡引入MINMOD斜率限制器;提出了虚拟边界的处理方法,实现了计算区域的所有节点和边界的统一计算。计算分析表明,虚拟边界法既保证了计算结果的精确性,又避免了边界处理的复杂性;一阶Godunov格式与传统的特征线法计算结果一致;当库朗特数小于1时,一阶Godunov格式和特征线法的瞬变压力可能出现严重的数值耗散,但二阶Godunov格式可有效抑制数值衰减从而得到更为准确稳定的计算结果;在马赫数很小的情况下,对流项对模拟结果的影响可忽略。     

von Neumann stability analysis of first-order accurate discretization schemes for one-dimensional (1D) and two-dimensional (2D) fluid flow equations

In literature, the von Neumann stability analysis of simplified model equations, such as the wave equation, is typically used to determine stability conditions for the non-linear partial differential fluid flow equations (Navier–Stokes and Euler). However, practical experience suggests that such simplistic stability conditions are grossly inadequate for computations involving the system of coupled flow equations. The goal of this paper is to determine stability conditions for the full system of fluid flow equations – the Euler equations are examined, as any conditions derived for the Euler equations will apply to the Navier–Stokes (NS) equations in the limit of convection-dominated flows. A von Neumann stability analysis is conducted for the one-dimensional (1D) and two-dimensional (2D) Euler equations. The system of equations is discretized on a staggered grid using finite-difference discretization techniques; the use of a staggered grid allows equivalence to finite-volume discretization. By combining the different discretization techniques, ten solution schemes are formulated – eight solution schemes are considered for the 1D Euler equations, and two schemes for the 2D Euler equations. For each scheme, error amplification matrices are determined from the stability analysis, stable and unstable regimes are identified, and practical stability limits are predicted in terms of the maximum-allowable CFL (Courant–Friedrichs–Lewy) number as a function of Mach number. The predictions are verified for selected schemes using the Riemann problem at incompressible and compressible Mach numbers. Very good agreement is obtained between the analytically predicted and the “experimentally” observed CFL values. The successfully tested stability limits are presented in graphical form, which offer a viable alternative to complicated mathematical expressions often reported in published literature, and should benefit everyday CFD (Computational Fluid Dynamics) users. The stability regions are used to discuss the effect of time integration (explicit vs. implicit), density bias in continuity equation and momentum convection term linearization on stability. A comparison of the predicted stability limits for 1D and 2D Euler equations with commonly-used stability conditions arising from the wave equation shows that the stability thresholds for the Euler equations lie well below those predicted by the wave equation analysis; in addition, the 2D Euler stability limits are more restrictive as compared to 1D Euler limits. Since the present analysis accounts for the full system of fluid flow (Euler) equations, the derived stability conditions can be used by CFD practitioners to estimate a timestep or CFL number to guide the stability of their computations.     

A finite difference/finite element technique with error estimate for space fractional tempered diffusion-wave equation

An efficient numerical technique is proposed to solve one- and two-dimensional space fractional tempered fractional diffusion-wave equations. The space fractional is based on the Riemann–Liouville fractional derivative. At first, the temporal direction is discretized using a second-order accurate difference scheme. Then a classic Galerkin finite element is employed to obtain a full-discrete scheme. Furthermore, for the time-discrete and the full-discrete schemes error estimate has been presented to show the unconditional stability and convergence of the developed numerical method. Finally, two test problems have been illustrated to verify the efficiency and simplicity of the proposed technique.     

基于IDDES方法的模型尺度和实尺度VLCC阻力预报与流场分析

随着CFD技术的发展和计算机运算能力的提高,CFD在船舶设计中发挥着越来越重要的作用。目前CFD对于船舶阻力的计算基本集中在模型尺度,一方面因为实尺度缺乏相关的实验数据,导致缺乏对实尺度高雷诺数下近壁面湍流模型和壁面函数的探索;另一方面也是因为在实尺度计算中,非定常特征更加明显,数值计算的复杂性会大大增加,传统的RANS方法处理起来较为困难。该文应用基于OpenFOAM开发的船舶与海洋工程水动力求解器naoe-FOAMSJTU,应用改进的DES模型—IDDES,采用CFD方法同时对模型尺度和实尺度的32万吨VLCC进行阻力预报,并分别与RANS的计算结果、实验结果/三因次换算结果进行比较分析。在实尺度计算中考虑到表面粗糙度的影响,采用带粗糙度补贴的壁面函数进行近壁面处理。该文探讨了采用IDDES方法在船模和实船阻力预报中的可行性,同时也对实尺度和模型尺度下的流场进行了讨论与对比分析。     

基于MPS方法数值模拟三维LNG液舱的晃荡问题

该文基于自主开发的无网格粒子方法求解器MLParticle-SJTU,将MPS方法(moving particle semi-implicit)应用到三维LNG液舱的晃荡问题中,分别研究了LNG液舱在单自由度纵摇和横摇激励下,装载高度和激励频率对液舱晃荡作用的影响。首先,对装载高度为70%H的LNG液舱在单自由度纵摇和横摇激励下的晃荡问题分别进行了数值模拟,并将计算结果与实验结果进行比较,验证了MPS方法的可靠性。其次,对比不同装载高度,不同激励频率下液舱晃荡的拍击压力和流场分布情况,分析了装载高度和激励频率对晃荡作用的影响,并分析了一阶固有频率和共振频率随装载高度的变化规律。数值结果表明:激励频率对晃荡幅度影响较大;当激励频率在一阶固有频率附近时,会发生剧烈的晃荡现象;52.5%H为危险装载高度,在共振频率下,产生的拍击压力最大。     

矿井通风网络解算软件研究综述

通过对国内外网络通风软件资料研究,围绕网络解算软件的理论基础、功能模块、主要研究方向等进行了综述.阐述了通风网络软件的发展现状及完善过程,总结了网络解算的发展特点,为矿井通风网络解算软件设计人员提供了一定参考.     

炼铁配矿集成配比优化模型的应用研究

针对高炉炼铁中入炉前原料和燃料生产成本存在的问题,以实际生产数据为基础,研究分步配比优化模型和集成配比优化模型的应用,并比较了两种配矿配比优化模型的炼铁生产成本。结果表明,分步配比优化模型达到分步最优却不一定能达到全局最优,集成配比优化模型较之分步配比优化模型,其应用效果可实现炼铁成本最低。