Numerical Method for Solving a Premixed Laminar Flame

A splitting-up method, which splits the chemical kinetic terms from the flow terms, is presented to solve time-dependent, one-dimensional, laminar, premixed flame problems. An example for studying the development of an ozone decomposition flame is calculated. A movable boundary technique is adopted, so that the number of grid points can be significantly reduced. Special care is taken to maintain the accuracy of the solution. The results are checked in many ways. All checks show that the present method is satisfactory.     

两种互不相溶流体在竖直的波状壁面和平行的平面壁面间作不稳定的混合对流传热

分析粘性、不可压缩、互不相溶流体,在竖直的波状壁面和光滑的平面壁间,传热传质混合对流的组合效应.得到无量纲控制方程的摄动解:0阶的均值部分和1阶的摄动部分.将所得到的1阶量,用小波长摄动级数展开,出现按指数阶分类的方程组.得到了0阶和1阶的解析表达式及其整体解,通过数值计算,用图形表明流体流动的显著特征以及传热特性.界面上应用适当的匹配条件,使分离的解相匹配.还针对控制参数的不同变化,分析了剪应力和Nusselt数的变化.发现Grashof数、粘性比、宽度比和导电率,对平行于流动方向的速度是有利的,对垂直于流动方向速度的影响正相反.     

粘性流体间夹有多孔介质时的非定常流动及其热传导

粘性流体间夹有多孔介质,流经壁面温度等温的水平管道时,研究其非定常振荡流动及其热传导问题.多孔介质中的流动采用Brinkman方程模型.通过集中非周期项和周期项,将偏微分的控制方程转化为常微分方程,并利用边界和界面条件,找到了每个区间的闭式解.数值计算了各种物理参数,如多孔性参数、频率参数、周期频率参数、粘度比、热传导系数比和Prandtl数,对速度和温度场的影响,并给出相应的图形.此外,导出了壁顶和壁底处的热传递率并用表格列出.     

A Numerical Method for Solving Matrix Coefficient Heat Equations with Interfaces

In this paper, we propose a numerical method for solving the heat equations with interfaces. This method uses the non-traditional finite element method together with finite difference method to get solutions with second-order accuracy. It is capable of dealing with matrix coefficient involving time, and the interfaces under consideration are sharp-edged interfaces instead of smooth interfaces. Modified Euler Method is employed to ensure the accuracy in time. More than 1.5th order accuracy is observed for solution with singularity (second derivative blows up) on the sharp-edged interface corner. Extensive numerical experiments illustrate the feasibility of the method.     

纳米流体强化传热问题的高效算法设计及其高精度数值模拟

对周期性温度边界条件下方腔内Copper-水纳米流体的对流传热问题建立了完全四阶高精度紧致差分格式,并探讨了该格式高效算法设计,同时引入伪时间导数项采用Von Neumann方法证明了格式的绝对稳定性.研究了不同Ri数下纳米颗粒体积分数、左右边界温度的正弦振幅比和相位偏差对纳米流体传热效率的影响.数值结果表明,对于给定的Ri数,随着纳米颗粒体积分数的增大和边界温度的正弦振幅比的增加,纳米流体的传热效果会显著增强,而相位偏差只影响方腔右侧的温度分布.     

热传导率对不同传导参数下幂律非Newton流体流经连续伸展表面时热传导的影响

在一个具有吸入/吹出功能、幂律变化的伸展表面上,分析了二维稳定非Newton流体的流动.假定热传导率按温度的线性函数变化.将控制方程无量纲化后,用Runge-Kutta法进行数值求解.将该问题的一个特例所得到的一些结果,与以前发表的结果相比较,发现两者有着很好的一致性.考虑两种情况,一种对应着致冷的表面温度,另一种对应着均匀的表面温度.数值结果显示,对上述两种情况,可变热传导参数β,传质参数d和幂律指数n,对温度分布和Nusselt数有着重大的影响.     

A Stable and Accurate Numerical Method to Calculate the Motion of a Sharp Interface Between Fluids

Present address: Department of Applied Mathematics, University of Adelaide, G.P.O. Box 498, Adelaide, South Australia 5001. A spectrally accurate numerical method, which is also simpleto implement, is derived to calculate the motion of a fluidinterface. A numerical instability, typical of algorithms forthis problem, is investigated via a linearizing approximationwhich shows that a trivial adjustment of the algorithm rendersit numerically stable while retaining high accuracy. To testfor the correct implementation of the algorithm, non-linearsimultaneous equations are formulated using time derivativeinformation only from the coded procedure, whose solutions describeprogressive interfacial waves of permanent form. The behaviourof this type of algorithm when variations in the point spacingoccurs along the interface is investigated and found to cause"scattering" of travelling wave modes.     

A Numerical Treatment of One-dimensional Models of Radiative Heat Transfer in Co-current Tube Furnaces

A model of a top-fired furnace, such as is used in chemicalindustrial plants, is described. The model gives rise to a systemof first-order differential equations, with boundary conditionsat both the top and bottom of the furnace. This also involvesa non-linear coupling of the radiation field to the energy ofthe gases flowing. Published accounts of this problem make useof shooting methods which converge extremely slowly. An alternativemethod will be described in which the radiative field equationsare solved by an algorithm of Grant and, to deal with the non-linearitiesof the system, a generalized Newton-Raphson method is employed.     

非线性多层渗流系统的数值方法及其应用

对多层非线性渗流系统提出适合并行计算的迎风分数步差分格式，利用变分形式、能量方法、差分算子乘积交换性、高阶差分算子的分解、先验估计的理论和技巧，得到收敛性的最佳阶的误差估计．该方法已成功的应用到油资源渗流力学运移聚集数值模拟的生产实际中．     

A Simple Analytical and Numerical Approach for Pricing Compound Options

A compound option is simply an option on an option. In this short paper, by using a martingale technique, we obtain an analytical formula for pricing compound European call options. Numerical results are given to explain some economic phenomenon.     

Weak Convergence of a Numerical Method for a Stochastic Heat Equation

Weak convergence with respect to a space of twice continuously differentiable test functions is established for a discretisation of a heat equation with homogeneous Dirichlet boundary conditions in one dimension, forced by a space-time Brownian motion. The discretisation is based on finite differences in space and time, incorporating a spectral approximation in space to the Brownian motion.     

热传导方程的均匀化方程的混合元方法

用混合有限元方法讨论稳态热传导问题的均匀化方程.给出了一种矩形剖分下的混合元格式,该格式具有各向异性特征,即剖分不满足正则性条件时也收敛,应用各向异性插值定理给出了误差分析.     

A Numerical Method for Conformal Mapping

A method is developed for constructing the conformal map ofa distorted region onto a rectangle. A discrete Fourier transformis used to map the boundary of the region onto the boundaryof the rectangle; the resulting equations may be solved usinga fast Fourier transform algorithm. The map for internal pointsmay then be constructed using a standard Laplace equation solver.The method is computationally competitive, and is applicableto field problems, for instance in fluid mechanics.     

Finite Velocity of the Propagation of Perturbations for a Class of Non-Newtonian Fluids

In this paper, we consider the initial boundary value problem of a class of non-Newtonian fluids. We obtain that finite velocity of the propagation of perturbations.     

带间断扩散系数热传导方程的高精度数值模拟方法研究

针对热传导方程在间断扩散系数处的数值求解困难,作者已经提出了"孪生逼近"自适应方法.本文以一维问题为例,推广热传导方程解的内蕴连续性到高阶,进而研究构造了更高精度,更经济的"孪生逼近"算法,并用数值结果进行了检验.     

A Mixed Method for the Elastoplastic Torsion Problem

In this paper a mixed formulation for the elastoplastic torsionproblem is given. This formulation is discretized with the finiteelements of Raviart & Thomas (1977) and error estimatesare obtained. For solving the (non-linear) approximated probleman iterative algorithm is proposed and analysed.     

求解非线性不适定的混合Newton-Tikhonov迭代法

鉴于Newton型方法在实际计算中计算量可能非常大,因此提出了一种一步Newton结合若干步简化Newton的混合Newton-Tikhonov方法,并且在一定条件下证明了该方法的收敛性和稳定性.数值试验表明,在减少计算量方面该方法相对于经典的Newton方法有明显的改善.