基于微可压液体的统一对流扩散型流体力学方程组

为了表达上的方便及求解格式的统一,通常采用统一的方程形式来表达连续方程,动量方程、能量方程、湍动能方程和耗散方程等.除了连续方程外,其他方程都可以写成对流扩散方程的形式,由于没有扩散项,连续方程比较特别,也相对不便处理.在微可压液体区,通过合理的数学推导,不作任何近似、假定与简化,本文得到一套全新的连续方程形式.该新方程以压力为未知变量,是对流扩散型的,使得所有的流体动力学方程组都具有完全统一的方程形式.     

辐射扩散方程的自适应坐标变换方法

借鉴自适应坐标变换流体力学方法和其他一些有益工作，研究辐射扩散方程的自适应坐标变换方法，并考虑辐射扩散和流体力学耦合的辐射流体力学问题。对辐射扩散方程和一般二维对流扩散方程，从积分和微分形式出发，导出自适应坐标变换下的等价形式，对数值离散格式进行初步讨论。对二维三温辐射扩散方程，采用时空有限体积方法，进行数值离散；利用局部函数近似离散扩散算子。利用合理的进程分裂，简化耦合问题的计算。     

对流扩散方程的格点模型

推广流体力学的格点法解一般的数学物理方程,建立了一维对流扩散方程的简单和复杂的格点模型,并利用此模型模拟了几种不同初边值条件下的对流扩散方程     

对流扩散方程的涡区分离解法

对流扩散方程是流体计算中一个基本方程,常用的数值方法导至解一个高阶的代数方程组,要求较大的存贮量和较长的计算时间。本文提出一种涡区分离解法,它利用对流扩散方程的迎风性质,把涡区从对流支配区分离出来,仅在各个涡区建立代数方程组并求解。而在对流支配区,则充分利用其抛物性,只需采用显式格式进行计算。由于在各涡区建立的这些方程组阶数和带宽都较小,因此要求存贮量较小,计算速度较快。对于雷诺数较大,涡区范围较小的问题,该方法特别有效。     

对流扩散方程的指数型摄动差分法

改进了作者所提出的对流扩散方程四阶指数型摄动差分格式,并阐明其在高Reynolds数适应性和节省计算量方面的显著优点。指数型摄动差分法经改进后具有较为简便的形式,克服了其他紧致高阶格式不能使用于高Reynolds数问题的致命弱点。文中针对计算流体力学的基本困难,作一至三维流动模型方程和自然对流传热问题的精细计算,且以双精制算法检验格式的四阶精度,表明摄动差分法能在较粗的网格下给出相当准确的结果,十分显著地节省计算机时,并对"激波"和"边界层"等高Reynolds数效应有极高的分辨能力。     

对称TVD差分格式的构造及其应用

本文从ＧＣＩＲ差分格式出发，通过附加中心加权形式的反扩散流量，构造出一类具有二阶精度的对称型ＴＶＤ格式以及相应的一般形式的隐式格式，并针对双曲型方程组问题进行了讨论。同时文中还采用这类格式求解Ｅｕｌｅｒ方程，成功地数值计算了具有激波的流动问题。     

自适应结构网格上扩散方程隐式时间积分算法及其应用

提出一种自适应结构网格(SAMR)上求解扩散方程的隐式时间积分算法.该算法从粗网格到细网格逐层进行时间积分,通过多层迭代同步校正保证粗细界面的流连续和计算区域的扩散平衡.分析算法复杂度,并给出评估算法低复杂度的准则.典型算例表明,相对于一致加密情形,本文算法能够在保持相同计算精度的前提下,大幅度降低网格规模和计算量,且具有低复杂度.将算法应用于辐射流体力学数值模拟中非线性扩散方程组求解,相对于一致加密网格,SAMR计算将计算量下降一个量级以上,计算效率提高33.2倍.     

改进的节块展开方法求解圆柱几何对流扩散方程

为高效求解球床高温气冷堆物理-热工耦合问题,发展改进节块展开法求解圆柱几何下的对流扩散方程.针对圆柱几何和对流扩散方程的特殊性,采用三阶多项式和指数函数作为r向横向积分方程的展开函数,在节块展开法的框架下高效求解对流扩散方程.数值验证表明,改进的节块展开方法具有固有的迎风特性,在使用粗网节块时依然能保持稳定性和较高的计算精度.     

混合Krylov子空间算法及其应用

给出了一种适合二维三温辐射流体力学能量方程的大型稀疏线性代数方程组的混合迭代算法.计算结果显示,该算法解二维三温辐射流体力学能量方程的大型稀疏线性代数方程组比原有算法快4倍左右;原有算法不收敛时,该算法收敛;各物理量也符合得很好.     

基于非结构网格的不可压流动耦合求解器

采用非结构化网格有限容积法求解了不可压N-S方程组,对流项采用GAMMA格式,扩散项采用二阶中心差分格式建立离散方程,用SOAR算法处理压力与速度的耦合关系,得到了一种求解不可压N-S方程的非结构网格耦合求解器。通过方腔顶盖驱动流、后台阶绕流以及方腔自然对流等几个典型的算例,考察了求解器的计算精度及收敛特性,并与SIMPLE算法进行了比较,结果表明该求解器是有效可行的。     

THE FLUID THEORY OF SELF-SUSTAINING MAGNETICALLY CONFINED ELECTRON CLOUDS (Ⅰ) FLUID EQUATIONS

In this paper the axisymmetrical self-sustaining magnetically confined electron clouds are studied by means of the fluid theory.In the electron clouds which supported by the Penning discharge the property of motion of electrons can be described by the fluid equations:continuity equation,momentum equation,energy equation,Poisson equation and heat transfer equation.The problems of the diffusion and escape of electrons and the energy transport in the electron clouds are discussed.     

Symmetry of Equations with Convection Terms

Abstract

We study symmetry properties of the heat equation with convection term (the equation of convection diffusion) and the Schrödinger equation with convection term. We also investigate the symmetry of systems of these equations with additional conditions for potentials. The obtained results are applied to construction of exact solutions of the system of the Schrödinger equation with convection term and the Euler equations for potentials.     

求解对流扩散方程的紧致修正方法

提出了求解对流扩散方程的紧致修正方法,该方法是在低阶离散格式的源项中,引入紧致修正项,从而构造高阶紧致修正格式,并进行求解.采用紧致修正方法对典型的对流扩散方程进行计算.结果表明,紧致修正方法虽然与二阶经典差分方法建立在相同的结点数上,但紧致修正方法的精度与紧致方法的精度相同,均具有四阶精度.所以紧致修正方法可以在少网...     

Mass,momentum and energy conserving (MaMEC) discretizations on general grids for the compressible Euler and shallow water equations

The paper explains a method by which discretizations of the continuity and momentum equations can be designed, such that they can be combined with an equation of state into a discrete energy equation. The resulting ‘MaMEC’ discretizations conserve mass, momentum as well as energy, although no explicit conservation law for the total energy is present. Essential ingredients are (i) discrete convection that leaves the discrete energy invariant, and (ii) discrete consistency between the thermodynamic terms. Of particular relevance is the way in which finite volume fluxes are related to nodal values. The method is an extension of existing methods based on skew-symmetry of discrete operators, because it allows arbitrary equations of state and a larger class of grids than earlier methods.The method is first illustrated with a one-dimensional example on a highly stretched staggered grid, in which the MaMEC method calculates qualitatively correct results and a non-skew-symmetric finite volume method becomes unstable. A further example is a two-dimensional shallow water calculation on a rectilinear grid as well as on an unstructured grid. The conservation of mass, momentum and energy is checked, and losses are found negligible up to machine accuracy.     

反常输运现象中的分数阶扩散方程

 根据连续性方程,可以得到分形上的标准扩散方程。然而这个标准扩散方程并不能真正描述分形介质中的反常扩散,其根源在于分形介质中的扩散具有记忆效应,为了得到更普遍的扩散方程,通过讨论早期提出的扩散方程的缺陷,可以得到分数阶扩散方程,并且更具有普遍性。     

DIMENSIONAL METHOD TO SOLVE THE DIFFUSION CONVECTION EQUATION OF SOLAR COSMIC RAYS

Physical processes of the propagation of the solar cosmic rays in the interplanetary space include the diffusion in interplanetary disordered magnetic fields and the convection in solar winds. Dimensional method can be applied to solve those equations convertible into Bessel equation, the results obtained are identical with those solved by the commonly used separate variable method. In order to derive an analytic solution to the diffusion convection equation in an unbounded, uniform medium, two dimensionless parameters reflecting the diffusion and convection characteristics of the particles are introduced. In the diffusion dominated case, the solution is similar in form to the diffusion of a source moving with the convection velocity and is modified by another convection term, which can be expanded into a power series of the convection parameter with coefficients composed of the generalized hypergeometric function series of the diffusion parameter. This solution has a clear physical meaning, and can suitably be used in the discussion of the rise phase characteristics of the solar cosmic rays from medium to high energies （E_p≥10¹ MeV）.     

Mass conservative finite volume discretization of the continuity equations in multi-component mixtures

The Stefan–Maxwell equations for multi-component diffusion result in a system of coupled continuity equations for all species in the mixture. We use a generalization of the exponential scheme to discretize this system of continuity equations with the finite volume method. The system of continuity equations in this work is obtained from a non-singular formulation of the Stefan–Maxwell equations, where the mass constraint is not applied explicitly. Instead, all mass fractions are treated as independent unknowns and the constraint is a result of the continuity equations, the boundary conditions, the diffusion algorithm and the discretization scheme. We prove that with the generalized exponential scheme, the mass constraint can be satisfied exactly, although it is not explicitly applied. A test model from the literature is used to verify the correct behavior of the scheme.     

Supernova-Explosion Mechanism Involving Neutrinos

A major part of the energy released upon the gravitational collapse of massive-star cores is carried away by neutrinos. Neutrinos play a crucial role in collapsing supernovae (SNe). At the present time, mathematical models of core-collapse SNe are based on multidimensional gas dynamics and thermonuclear reactions, whereas the neutrino transport is frequently treated in simplified way. An accurate analysis of neutrinos in a spherically symmetric gravitational collapse is performed on the basis of Boltzmann kinetic equations including all weak-interaction reactions with exact quantum-mechanical matrix elements. The role of multidimensional effects is studied bymeans of multidimensional gas dynamics allowing for the neutrino transport via diffusion treated by employing flux limiters. The possibility of largescale convection, which is of interest both from the point of view of explaining a type II supernova (SN) and from the point of view of implementing an experiment aimed at detecting possible energetic (?10 MeV) neutrinos from an SN, is discussed. Thermonuclear burning leads to the explosion of a type I SN. A hot central region and the subsequent large-scale convection may also play an important role in the SN mechanism. If neutrinos and convection play a key role for a type II SN, then, in order to explain gamma radiation from product radioactive elements, convection is of importance in the case of SNe belonging to both types. In addition, convection may be important for bright type I SNe. Original methods are presented for multidimensional gas dynamics involving thermonuclear burning and for multitemperature gas dynamics involving radiative transfer.     

Spectral element formulations on non-conforming grids: A comparative study of pointwise matching and integral projection methods

Pointwise matching (PM) and integral projection (IP) methods are two widely used techniques to extend the classical weak formulations to include non-conforming grids. We present spectral element formulations on polynomial (p-type) and geometric (h-type) non-conforming grids using both the PM (also known as the Constrained Approximation) and IP (also known as the Mortar Element) methods. We systematically compare the convergence characteristics of PM and IP methods for diffusion, convection, and convection–diffusion equations. Consistency errors due to the non-conforming formulations of the diffusion equation result in convergence problems for the PM method using the maximum rule. Both non-conforming formulations for the unsteady convection operator result in eigenvalue spectrum with positive real values, causing convergence problems due to the consistency errors. However, small “physical” diffusion in the convection–diffusion equation eliminates these problems, resulting in spectral convergence for both methods. Encouraged by this, we present spectral element formulations for incompressible Navier–Stokes equations using PM and IP methods on p-type and h-type non-conforming grids, and demonstrate spectral convergence for unsteady and steady test cases. Results for two-dimensional lid-driven cavity flow at Re = 1000 are also presented.     

格子Boltzmann方法模拟自然对流作用下融化传热过程

建立自然对流作用下融化的格子Boltzmann双分布函数模型,根据非线性对流扩散方程的格子Boltzmann模型理论提出一个新的表征融化温度场的分布函数演化方程,并通过变松弛时间方法处理固液两相变热物性传热问题.应用模型对热传导融化及自然对流融化特别固液变热物的融化过程进行模拟.模拟结果与分析解、经典的关联式结果吻合较好,模型的正确性得到了验证.模拟结果表明,自然对流对融化传热过程有着重要的影响,此外固相热传导也对融化传热、融化速率及固液两相温度分布都有一定影响.