材料热物性与热源强度辨识的改进遗传算法

建立二维非线性导热逆问题(IHCP)的数学模型.通过对基本遗传算法逐步改进得到三种不同改进阶段的遗传算法,分别用于反演导热问题中材料的导热系数及其内部热源强度,并比较遗传算法在各改进阶段用于求解导热逆问题时的收敛速度与求解精度,寻求一种使导热逆问题求解效率与计算精度更高的遗传算法改进策略.结果表明:提出的遗传算法改进策略达到了预期目的.     

二维扩散方程的局部二阶线性保极值节点计算方法及应用

对一般四边形网格设计一种优化的节点控制体, 并构造了一种扩散方程的保极值二阶收敛的局部线性节点计算格式(优化控制体节点格式, VOC格式)。在网格不出现异常节点的情况下, 证明VOC格式是保极值、线性精确和二阶收敛的。而且在均匀的矩形网格上, 修正的逆距离加权格式与VOC格式等价, 从而对间断系数问题也是局部二阶收敛的。VOC格式可以用于单元中心型线性扩散格式和保正格式的节点值计算。数值算例表明对扭曲网格上的间断系数问题, VOC格式是二阶收敛的。采用VOC格式计算节点值的线性九点格式具有线性精确性和二阶收敛性, 采用VOC格式的保正格式也具有二阶收敛性。     

一个二阶单调迎风格式及对不定常激波反射的计算

本文介绍了Van Leer提出的一个二阶单调迎风格式。此格式有效地克服了通常二阶穿行法格式的激波后过跳现象,同时保持较窄的间断过渡区。本文主要算例是黎曼问题及平面一维强爆炸波遇固壁后正反射问题。我们改进了单调化的算法,给出了适当处理某种固壁条件的方法,因此得到了较好的数值结果。本文更正了Van Leer文章中一个主要公式及稳定性条件等的不妥之处。     

基于改进布谷鸟算法识别瞬态热传导问题的导热系数

基于改进布谷鸟算法反演瞬态热传导问题随温度变化的导热系数.采用Kirchhoff变换将非线性热传导问题转换为线性热传导问题,使用边界元法求解瞬态热传导正问题.将导热系数的反演转化为函数表达式中未知参数的反演,使用改进布谷鸟算法求解未知参数.与共轭梯度法相比,改进布谷鸟算法对迭代初值不敏感;与布谷鸟算法相比,改进布谷鸟算法迭代次数大大减少.数值算例表明对改进布谷鸟算法,增加测点数量迭代次数增加;增加鸟巢数量迭代次数减少;减小测量误差计算结果更精确,同时迭代次数更少.数值算例验证了改进布谷鸟算法反演导热系数的准确性和有效性.     

扩散方程计算方法研究进展

描述多维内爆动力学过程的非平衡辐射流体力学问题包括电子、离子、光子（三温）热传导或辐射多群扩散等,它们具有多介质、大变形、高温、高压与强非均匀性等特点,其方程组具有强间断、强耦合和强非线性等特征。现有的九点格式和多点通量逼近方法（MPFA）在任意四边形网格上物理量计算出负,且九点格式中节点值计算不准确。全隐Picard迭代方法仅具有一阶收敛速度;     

Lateral Epitaxy Overgrown (LEO) GaN 导热系数的数值研究

利用修正的Callaway模型对含杂质、位错、以及同位素的LEO GaN的导热系数进行了研究,计算表明同位素对LEO GaN的导热系数影响较大,而位错和杂质大于一定值时其值才对导热系数产生影响.     

液相饱和度对多孔介质稳态导热系数的影响

在非饱和含湿多孔介质传热传质的过程中,由于湿分迁移的存在,使得真实导热系数的测量和处理存在争议。为此,运用有限元方法,求解了二维稳态条件下非饱和含湿多孔体特征单元的温度和热流密度,给出了不同液相饱和度时的有效导热系数。结果表明,对于通常的导热能力固体远大于液体、液体远大于气体的情形,随着液相饱和度的增加,多孔介质的导热系数先迅速增加,然后逐渐趋于平稳。     

含湿建筑材料的导热系数

本文报道了用常功率平面热源法测定含湿加气混凝土砌块导热系数和导温系数的试验结果。发现实测到的总当量导热系数λ随含湿量的增加而单调地递升,名义导温系数α随含湿量的变化曲线却在低含湿量区出现明显的拐点和极小值。文中,对含湿建筑材料在温度梯度下的湿—热迁移机理作了初步探讨,并给出了一种半经验方法,提供了实用的算图(图8)和进行温度修正的式(14)和(15),可由式(13)从实测的总当量导热系数λ中扣除湿迁移影响,由此得到的真导热系数λ_0和含湿量之间呈现线性关系(图7)。     

基于DISLab温度传感器的导热系数测定

对采用热电偶测量导热系数的实验进行改进,利用DISLab温度传感器测金属盘达到平衡的温度和散热盘的温度,解决了传统的导热系数测定时误差较大的问题。实验表明,该实验操作简单,精度高,具有明显的优势。     

光纤温度传感器实验的改进与分析

本文利用价格低廉的1310 nm商用光纤分束器、铝箔导热等对光纤温度传感器实验装置进行了改进,并测量了改进后传感器的温度系数,发现改进后的温度系数更加稳定,导热条件对温度系数的测量影响较大.最后对此实验的教学提出了建议.     

间断有限元方法求解一维非平衡辐射扩散方程

研究一维非平衡辐射扩散方程的数值方法.通过求解间断系数热传导方程的广义黎曼问题,得到一种带加权数值流量,基于该数值流量构造了一类新型的间断有限元方法.在时间离散上采用向后Euler方法,形成的非线性方程组采用Picard迭代求解.数值试验表明该方法具有捕捉大梯度的能力,而且能适应扩散系数间断的情形.     

Direct discontinuous Galerkin method for the generalized Burgers—Fisher equation

In this study, we use the direct discontinuous Galerkin method to solve the generalized Burgers-Fisher equation. The method is based on the direct weak formulation of the Burgers-Fisher equation. The two adjacent cells are jointed by a numerical flux that includes the convection numerical flux and the diffusion numerical flux. We solve the ordinary differential equations arising in the direct Galerkin method by using the strong stability preserving Runge-Kutta method. Numerical results are compared with the exact solution and the other results to show the accuracy and reliability of the method.     

解三维扩散方程的积分内插法格式

研究三维扩散方程的数值模拟.在非正规六面体网格上,使用积分内插法建立扩散方程差分格式,涉及到27个相邻网格,适用于大变形网格上带间断系数的拟线性扩散方程的计算.叙述差分格式的建立,推导通量流和网格顶点温度的计算公式,给出了数值试验结果.     

Newton-conjugate-gradient methods for solitary wave computations

In this paper, the Newton-conjugate-gradient methods are developed for solitary wave computations. These methods are based on Newton iterations, coupled with conjugate-gradient iterations to solve the resulting linear Newton-correction equation. When the linearization operator is self-adjoint, the preconditioned conjugate-gradient method is proposed to solve this linear equation. If the linearization operator is non-self-adjoint, the preconditioned biconjugate-gradient method is proposed to solve the linear equation. The resulting methods are applied to compute both the ground states and excited states in a large number of physical systems such as the two-dimensional NLS equations with and without periodic potentials, the fifth-order KdV equation, and the fifth-order KP equation. Numerical results show that these proposed methods are faster than the other leading numerical methods, often by orders of magnitude. In addition, these methods are very robust and always converge in all the examples being tested. Furthermore, they are very easy to implement. It is also shown that the nonlinear conjugate gradient methods are not robust and inferior to the proposed methods.     

On choosing a nonlinear initial iterate for solving the 2-D 3-T heat conduction equations

The 2-D 3-T heat conduction equations can be used to approximately describe the energy broadcast in materials and the energy swapping between electron and photon or ion. To solve the equations, a fully implicit finite volume scheme is often used as the discretization method. Because the energy diffusion and swapping coefficients have a strongly nonlinear dependence on the temperature, and some physical parameters are discontinuous across the interfaces between the materials, it is a challenge to solve the discretized nonlinear algebraic equations. Particularly, as time advances, the temperature varies so greatly in the front of energy that it is difficult to choose an effective initial iterate when the nonlinear algebraic equations are solved by an iterative method. In this paper, a method of choosing a nonlinear initial iterate is proposed for iterative solving this kind of nonlinear algebraic equations. Numerical results show the proposed initial iterate can improve the computational efficiency, and also the convergence behavior of the nonlinear iteration.     

An Inverse Source Problem with Sparsity Constraint for the Time-Fractional Diffusion Equation

In this paper, an inverse source problem for the time-fractional diffusion equation is investigated. The observational data is on the final time and the source term is assumed to be temporally independent and with a sparse structure. Here the sparsity is understood with respect to the pixel basis, i.e., the source has a small support. By an elastic-net regularization method, this inverse source problem is formulated into an optimization problem and a semismooth Newton (SSN) algorithm is developed to solve it. A discretization strategy is applied in the numerical realization. Several one- and two- dimensional numerical examples illustrate the efficiency of the proposed method.     

Enskog-Landau kinetic equation for multicomponent mixture. Analytical calculation of transport coefficients

The Enskog-Landau kinetic equation is considered to describe non-equilibrium processes of a mixture of charged hard spheres. This equation has been obtained in our previous papers by means of the non-equilibrium statistical operator method. The normal solution of this kinetic equation found in the first approximation using the standard Chapman-Enskog method is given. On the basis of the found solution the flows and transport coefficients have been calculated. All transport coefficients for multicomponent mixture of spherical Coulomb particles are presented analytically for the first time. Numerical calculations of thermal conductivity and thermal diffusion coefficient are performed for some specific mixtures of noble gases of high density. We compare the calculations with those ones for point-like neutral and charged particles. Received 10 June 1999 and Received in final form 15 October 1999     

Kinetic theory of dense fluids. II. The generalized Chapman-Enskog solution

In the second paper of this series we solve the kinetic equation proposed in the previous paper by a method following the spirit of Chapman and Enskog (generalized Chapman-Enskog method). The zeroth-order solution to the kinetic equation leads to the Euler equations in hydrodynamics for real fluids, and the first-order solution to the Navier-Stokes equations for real fluids. General formulas for transport coefficients such as viscosity and heat-conductivity coefficients are obtained for dense fluids, which are given in terms of time-correlation functions of fluxes conjugate to the thermodynamic forces. The results have the same formal structures as the time-correlation functions in linear response theory except for the collision operator appearing in place of the Liouville operator in the evolution operator for the system.     

适应强扭曲网格的扩散方程时空二阶精度计算

以全局支撑算子方法为基础,通过引入面通量,构造了具有局部模板点的时空二阶精度格式。对于大变形扭曲网格,格式采用法向修正技术和合理的单元角体积计算方法,可以保持通量的精确性。算例表明该格式在非凸网格上能够精确获得线性解; 在非光滑网格上可以达到时空二阶精度; 能够较好地保持对称性; 并适合于三维非结构网格上的求解。     

Numerical approximations for fractional diffusion equations via a Chebyshev spectral-tau method

In this paper, a class of fractional diffusion equations with variable coefficients is considered. An accurate and efficient spectral tau technique for solving the fractional diffusion equations numerically is proposed. This method is based upon Chebyshev tau approximation together with Chebyshev operational matrix of Caputo fractional differentiation. Such approach has the advantage of reducing the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical technique. We apply this general method to solve four specific examples. In each of the examples considered, the numerical results show that the proposed method is of high accuracy and is efficient for solving the time-dependent fractional diffusion equations.