TVD格式求解对流扩散方程的最优限制器研究

为探究不同通量限制器应用于TVD(Total Variation Diminishing)格式求解对流扩散方程时的适用性,基于3种典型的TVD格式与10种常用的通量限制器,分别求解了线性对流扩散方程、非线性对流扩散方程、拟线性对流扩散方程。数值结果表明,相比于MUSCL(Monotonic Upstream-centered Scheme for Conservation Laws)和MTVDLF(Modified TVDLF)格式,采用TVDLF(TVD Lax-Friedrichs)格式时,计算结果出现了较为严重的数值耗散;对MUSCL和MTVDLF格式进行具体分析发现,关于阶跃型纯对流问题,Superbee限制器的误差最小,Minmod误差最大。关于高斯型对流扩散问题,Minmod误差最大,Woodward误差最小。而关于阶跃型对流扩散问题及Burgers方程,限制器的类型对实验结果影响并不明显。     

传输扩散方程的差分格式

本文对传输扩散方程构造了两个带单参数的两层半显差分格式,证明了格式的绝对稳定性,对于初边值问题,计算是显式的。     

一阶、二阶导数耦合的紧致差分格式及其应用

在数值计算中可能遇到求解一阶导数和二阶导数耦合的微分方程,为了能用紧致差分格式进行计算,针对这样的方程,建立了考虑一阶、二阶导数耦合的紧致差分格式,利用这一方法可以直接对方程进行离散求解。通过具体算例,验证该类紧致差分格式的优越性,还将这类紧致差分格式运用到求解二维偏微分方程中。     

时间分数阶四阶扩散方程的显-隐和隐-显差分格式

时间分数阶四阶扩散方程是一类重要的发展型偏微分方程,其数值解的研究有重要的科学意义和工程实际价值.本文针对时间分数阶四阶扩散方程,研究一类显-隐(E-I)差分格式和隐-显(I-E)差分格式解法,该方法基于经典隐式和经典显式格式相结合构造而成,分析E-I和I-E两种差分格式解的存在唯一性、稳定性和收敛性.理论分析和数值试验结果证实本文E-I差分格式和I-E差分格式无条件稳定,具有空间2阶精度,时间2-α阶精度.在计算精度一致的要求下,E-I和I-E差分格式较经典隐式差分格式具有省时性,其计算时间相比古典隐格式减少约70%,研究表明本文格式求解时间分数阶四阶扩散方程是有效的.     

广义平均值差分格式在对流—扩散方程中的应用

§1.引言 从逼近的角度看,微分方程的各种数值方法均可认为是对解函数的某种方式的逼近。当解具有大梯度时,线性逼近的效果往往不好。一般的克服办法是细分网格或采用高阶多项式插值。本文考虑从非线性逼近的角度处理微分方程大梯度问题。前几年孙家昶导出广义平均值以及一类半线性数值微分公式,并且运用这种工具解常微分方程的初边值问题,取得良好效果。本文在此基础上对于对流—扩散方程用广义平均值构造了一种自适应的差分格式,使之具有根据解的局部性态选择格式的特点,并分析了格式的截断误差和所引入参数的选取,以及格式的稳定性和保单调性条件。对于一维及二维问题的一     

一类非线性延迟抛物偏微分方程的Crank-Nicolson型差分格式

对一类带有Dirichlet边界条件的延迟非线性抛物偏微分方程的初边值问题建立了一个Crank-Nicolson型的线性化差分格式,用离散能量法证明了该差分格式在L_∞范数下是无条件收敛的且是稳定的,其收敛阶为O(r~2+h~2).最后,用数值算例验证了理论结果.     

求解非线性Schroedinger方程的一个线性化紧致差分格式

通过对非线性项的局部外推,对非线性Schroedinger方程给出了一个线性化紧致差分格式,运用不动点定理和能量方法证明了格式的唯一可解性,文章还运用能量方法和数学归纳法,避开困难的先验估计,证明格式在空间方向和时间方向分别具有四阶和二阶精度,数值算例验证了格式的精度和数值稳定性．     

一类多参数的曲线细分格式

构造了一类收敛的多参数差分格式,根据细分格式和差分格式的关系以及连续性条件可得到任意阶连续的多参数曲线细分格式.通过选取合适的参数可以得到一些经典的曲线细分格式,如Chaikin格式、三次样条细分格式和四点插值格式等;同时设计了一种C1连续的不对称三点插值格式,可以生成不对称的极限曲线.给出了同阶差分格式线性组合的性质,从而可设计出更多收敛的多参数曲线细分格式.     

对起重机械安全保护装置起重量限制器的分析

起重机械安全保护装置是保障起重机械能够正常安全运行的重要措施,起重机械的安全保护装置多种多样,每一种保护措施都与起重机械的安全运行息息相关,笔者对安全保护装置中的起重量限制器进行分析与介绍,希望对起重机械的安全运行有所帮助。     

力矩限制器雷击浪涌测试、分析与改进

为了设计适应复杂电磁环境的力矩限制器,本文从雷击浪涌的测试标准入手,结合雷击浪涌实验结果,深入分析力矩限制器电源电路部分的功能,分析器件选型的实用方法,为实际工程应用中优化力矩限制器电磁兼容性能,优化硬件设计和器件选型提供理论和实验支撑。     

Solving Schemes for Computational Magneto-Aerodynamics

The electromagnetic force introduces a new physics dimension for enhancing aerodynamic performance of aerospace vehicles. In order to simulate interdisciplinary phenomena, the Navier–Stokes and Maxwell equations in the time domain must be integrated on a common frame of reference. For a wide range of applications from subsonic unmanned vehicles to hypersonic flight control, the resultant nonlinear partial differential equations offer a formidable challenge for numerical analysis. The experience and physical insight using the approximate Riemann and compact-differencing formulation as well as several temporal discritizations will be shared. The most recent development and advancement in numerical procedures for solving this system of governing equations are delineated     

TVD Fluxes for the High-Order ADER Schemes

In this paper we propose to use a TVD flux, instead of a first-order monotone flux, as the building block for designing very high-order methods; we implement the idea in the context of ADER schemes via a new flux expansion. Systematic assessment of the new schemes shows substantial gains in accuracy; these are particularly evident for problems involving long time evolution     

Analysis and Comparison of Replicated Declustering Schemes

Declustering distributes data among parallel disks to reduce the retrieval cost using I/O parallelism. Many schemes were proposed for the single-copy declustering of spatial data. Recently, declustering using replication gained a lot of interest and several schemes with different properties were proposed. An in-depth comparison of major schemes is necessary to understand replicated declustering better. In this paper, we analyze the proposed schemes, tune some of the parameters, and compare them for different query types and under different loads. We propose a three-step retrieval algorithm for the compared schemes. For arbitrary queries, the dependent and partitioned allocation schemes perform poorly; others perform close to each other. For range queries, they perform similarly with the exception of smaller queries in which random duplicate allocation (RDA) performs poorly and dependent allocation performs well. For connected queries, partitioned allocation performs poorly and dependent allocation performs well under a light load.     

Arbitrary High-Order Discontinuous Galerkin Schemes for the Magnetohydrodynamic Equations

In this paper, we propose a discontinuous Galerkin scheme with arbitrary order of accuracy in space and time for the magnetohydrodynamic equations. It is based on the Arbitrary order using DERivatives (ADER) methodology: the high order time approximation is obtained by a Taylor expansion in time. In this expansion all the time derivatives are replaced by space derivatives via the Cauchy-Kovalevskaya procedure. We propose an efficient algorithm of the Cauchy-Kovalevskaya procedure in the case of the three-dimensional magneto-hydrodynamic (MHD) equations. Parallel to the time derivatives of the conservative variables the time derivatives of the fluxes are calculated. This enables the analytic time integration of the volume integral as well as that of the surface integral of the fluxes through the grid cell interfaces which occur in the discrete equations. At the cell interfaces the fluxes and all their derivatives may jump. Following the finite volume ADER approach the break up of all these jumps into the different waves are taken into account to get proper values of the fluxes at the grid cell interfaces. The approach under considerations is directly based on the expansion of the flux in time in which the leading order term may be any numerical flux calculation for the MHD-equation. Numerical convergence results for these equations up to 7th order of accuracy in space and time are shown.     

超声速进气道流场的CFD数值仿真

进气道是航空推进系统的一个重要组成部分,进气道内的流场品质会显著影响发动机的性能.由于进气道内部流动的复杂性和其广泛的应用前景,进气道内的流动特性引起了人们广泛的关注.采用计算流体力学(CFD)方法,空间离散采用Harten-Yee的二阶迎风TVD格式,时间迭代采用隐式LU-SGS方法,数值求解Navier-Stokes(N-S)方程,对进气道内部流场进行了数值模拟,并研究了进气道内部流场的流场结构以及激波/边界层干扰问题.数值计算结果反映出了流场的基本物理现象,说明了所采用的研究方法是可行的.同时数值模拟结果对进气道的设计有一定的参考价值.     

Free radical polymerization in multilaminated microreactors: 2D and 3D multiphysics CFD modeling

This paper investigates the modeling of styrene free radical polymerization in two different types of microreactor. A multiphysics model which simultaneously takes into account the hydrodynamics, thermal and mass transfer (convection, diffusion and chemical reaction) is proposed. The set of partial differential equations resulting from the model is solved with the help of the finite elements method either in a 2D or a 3D approach. The different modeled microreactors are on one hand an interdigital multilamination microreactor with a large focusing section, and on the other hand a simple T-junction followed by a straight tube with three different radii. The results are expressed in terms of reactor temperature, polydispersity index, number-average degree of polymerization and monomer conversion for different values of the chemical species diffusion coefficient. It was found that the 2D approach gives the same results as the 3D approach but allows to dramatically reduce the computing time. Despite the heat released by the polymerization reaction, it was found that the thermal transfer in such microfluidic devices is high enough to ensure isothermal conditions. Concerning the polydispersity index, the range of diffusion coefficients over which the polydispersity index can be maintained close to the theoretical value for ideal conditions increases as the tube reactor radius decreases. The interdigital multilamination microreactor was found to act as a tubular reactor of 0.78 mm ID but with a shorter length. This underlines that the use of microfluidic devices can lead to a better control of polymerization reactions.     

全动舵铰链力矩计算的CFD数值仿真

在飞行器设计初期,舵面铰链力矩的预测主要依靠理论估算和试验测量的方法取得,随着CFD技术的发展,运用数值模拟方法预测舵面铰链力矩成为现实.使用二阶精度的Hahen-Yee空间离散格式和LU-SGS隐式时间推进方法计算了单独舵面以及弹身一舵面组合体外形的超音速绕流流场特性,并通过积分计算了单独舵面以及舵体组合体的压心位置和铰链力矩.考察了在不同来流马赫数、攻角和舵偏角状态下的压心位置和铰链力矩的变化.计算铰链力矩时用了两种不同的方法,第一种是直接对铰链轴进行压强积分计算,第二种方法是先求出压心位置和法向力,然后再计算铰链力矩,并对两种方法进行了对比分析.计算结果表明两种计算方法所得结果比较接近,验证了数值仿真的可行性,对舵面铰链力矩预测有很好的指导意义.     

换热器仿真动态数学模型计算方法比较

该文以石油、化工和火电厂常用的换热器为研究对象，对其仿真动态数学模型的算法进行了研究，重点讨论了梯形法、改进的欧拉法、四阶龙格一库塔法和动态因子法的数值解的稳定性、计算速度以及精度，从中选出最优算法。     

Using color-image maps to study collisions in the three-body problem

Color-image maps are generated through computer-based simulations to study the evolution of a system of three bodies interacting under classical gravitational forces. These image maps partition the set of possible initial-system configurations into regions that exhibit similar evolutionary characteristics. This resembles the technique used to produce color images of the Mandelbrot set. A restricted case of the three-body problem, in which the initial velocities of all three bodies are zero and the bodies are all of equal mass, is examined in detail. Image maps of the time to collision (assuming a finite radius) as a function of initial configuration are presented. Symmetries of the resulting maps are analyzed for invariants by means of transformations of scale.