扩散方程的有限方向差分方法

研究二维散乱点集上数值求解非线性扩散方程的有限方向差分方法。利用五个邻点信息构造具有最小模板的离散格式,并且离散系数具有显式表达式。另外,利用五点公式获得了间断问题物质界面的离散格式,该格式对界面流的计算具有近似二阶精度。不同计算区域及不同类型的离散点集上的计算结果验证了方法的有效性。     

扩散方程的有限方向差分方法（英文）

研究二维散乱点集上数值求解非线性扩散方程的有限方向差分方法。利用五个邻点信息构造具有最小模板的离散格式,并且离散系数具有显式表达式。另外,利用五点公式获得了间断问题物质界面的离散格式,该格式对界面流的计算具有近似二阶精度。不同计算区域及不同类型的离散点集上的计算结果验证了方法的有效性。     

具有TVD性质的三阶精度GODUNOV格式在粘性流场计算中的应用

本文发展了一种具有TVD性质的三阶精度的Godunov格式。隐式部分采用迎风对角线形隐式近似因式分解法。并引入了粘性通量的简化算法。显式部分采用三阶精度TVD格式。为进一步增强格式的稳定性及对间断的捕捉能力,在单元边界上构造Riemann问题。应用上述方法对某型涡轮高压级及压气机进行了数值模拟。     

比例边界有限元法在电机电磁场问题中的应用

将比例边界有限元法应用到电机磁场分析计算中,采用加权余量法推导无旋磁场的比例边界有限元方程及其离散格式,给出相邻子域公共边上内部节点磁位求解方法.以具有解析解的电机磁场问题为例进行计算和对比分析,验证离散格式的正确性和比例边界有限元法求解电机磁场的可行性,为该方法在电机磁场问题中的应用打下基础.     

基于界面修正的迭代并行计算方法

构造基于界面修正的迭代并行方法的一般途径是：将物理空间区域剖分成若干不重叠的块；在分块子区域的内边界上，采用某种显式格式计算出界面值作为预估值；然后采用某种隐式格式并行求解各个子块区域上的解，这里的隐式格式通常需要进行迭代求解(称为内迭代)；可在每一迭代步或几次迭代步结束时，利用已计算出的分块子区域内的(近似)解，在分块子区域内边界处利用隐式格式计算出在内边界处的校正值；随后再转入各个子块区域上的求解，该过程称为外迭代。与以往的并行差分格式不同，在求解的子区域上的定解问题时，可以仅仅在第一个(初始)迭代步求解时所需边界条件使用子区域内界面处的某种显式格式的解，在随后的迭代步中即可改用子区域内界面处的隐式修正格式的解。由此，至少可区分如下3类性质不完全相同的迭代并行格式。     

一种基于特征理论模拟凝聚炸药爆轰的单元中心型Lagrange方法

提出一种数值模拟凝聚炸药爆轰问题的单元中心型Lagrange方法.利用有限体积离散爆轰反应流动方程组,基于双曲型偏微分方程组的特征理论获得离散网格节点的速度与压力,获得的网格节点速度与压力用于更新网格节点位置以及计算网格单元边的数值通量.以这种方式获得的网格节点解是一种"真正多维"的理论解,是一维Godunov格式在二维Riemann问题的推广.有限体积离散得到的爆轰反应流动的半离散系统使用一种显-隐Runge-Kutta格式来离散求解：显式格式处理对流项,隐式格式处理化学反应刚性源项.算例表明,提出的单元中心型Lagrange方法能够较好地模拟凝聚炸药的爆轰反应流动.     

基于任意拉格朗日—欧拉型移动网格的反应流广义黎曼问题方法（英文）

提出一种在自由重映移动网格下的广义黎曼问题方法模拟反应流.该方法基于显式的自由重映移动网格广义黎曼问题的解.为保证在时间和空间上的高精度,应用广义黎曼问题方法构造数值通量.为保证反应区的高分辨率,采用变分法生成自适应移动网格.该方法不仅能够保证网格质量,而且能有效地避免任意拉格朗日—欧拉方法中由于显式重映过程而带来的数值误差.包括CJ爆轰及不稳定爆轰的数值实验说明该格式的精确性和鲁棒性,证明这种移动网格下的二阶广义黎曼问题方法可以较好地捕捉反应流的间断与光滑结构.     

基于任意拉格朗日—欧拉型移动网格的反应流广义黎曼问题方法

提出一种在自由重映移动网格下的广义黎曼问题方法模拟反应流.该方法基于显式的自由重映移动网格广义黎曼问题的解.为保证在时间和空间上的高精度，应用广义黎曼问题方法构造数值通量.为保证反应区的高分辨率，采用变分法生成自适应移动网格.该方法不仅能够保证网格质量，而且能有效地避免任意拉格朗日—欧拉方法中由于显式重映过程而带来的数值误差.包括CJ爆轰及不稳定爆轰的数值实验说明该格式的精确性和鲁棒性，证明这种移动网格下的二阶广义黎曼问题方法可以较好地捕捉反应流的间断与光滑结构.     

局部时间步长间断有限元方法求解三维欧拉方程

使用间断有限元方法求解三维流体力学方程.空间剖分采用非结构四面体网格,为了克服显格式在单元网格尺寸差别较大时计算效率低下的问题,在格式中采用局部时间步长技术(LTS),即控制方程在空间、时间上积分得到一种单步格式,既可以局部计算每个单元又避免了Runge-Kutta高精度格式处理三维问题时存储量过大的问题.为了提高流体力学方程计算精度,在计算单元边界的数值流通量时使用任意高阶精度方法(ADER).数值算例表明格式稳定有效.     

格子Boltzmann守恒型非平衡态的外推边界

针对非平衡态外推边界处理方法在某些条件下发生质量泄漏的问题,结合质量守恒定律对其进行修正,建立一种新的质量守恒型的边界处理格式.其基本思想是在边界处定义一个虚拟密度来修正平衡态分布函数,使得系统质量守恒.以重力作用下的密度场及磁流体模拟问题为例,利用该格式进行分析,讨论质量泄露问题的本质及各种因素的影响.通过对三种典型的流动:二维Poiseuille流、Couette流、Womersley流的模拟,验证该边界格式的计算精度和稳定性.     

螺线型爆磁压缩发生器的初始瞬态磁场分布

研究了螺线管型爆磁压缩发生器中金属套筒的一维磁扩散模型,分别导出了不同边界条件下的近似解析表达式,分析了瞬态磁场分布的特点,指出了经典趋肤深度计算公式的高频局限性,得出了能够同时反映高频与低频特性的磁场分布与相应趋肤深度的近似解析结果.     

Diffusion front capturing schemes for a class of Fokker–Planck equations: Application to the relativistic heat equation

In this research work we introduce and analyze an explicit conservative finite difference scheme to approximate the solution of initial-boundary value problems for a class of limited diffusion Fokker–Planck equations under homogeneous Neumann boundary conditions. We show stability and positivity preserving property under a Courant–Friedrichs–Lewy parabolic time step restriction. We focus on the relativistic heat equation as a model problem of the mentioned limited diffusion Fokker–Planck equations. We analyze its dynamics and observe the presence of a singular flux and an implicit combination of nonlinear effects that include anisotropic diffusion and hyperbolic transport. We present numerical approximations of the solution of the relativistic heat equation for a set of examples in one and two dimensions including continuous initial data that develops jump discontinuities in finite time. We perform the numerical experiments through a class of explicit high order accurate conservative and stable numerical schemes and a semi-implicit nonlinear Crank–Nicolson type scheme.     

Explicit TE/TM scheme for particle beam simulations

In this paper we propose an explicit two-level conservative scheme based on a TE/TM like splitting of the field components in time. Its dispersion properties are adjusted to accelerator problems. It is simpler and faster than the implicit version [I. Zagorodnov, T. Weiland, TE/TM scheme for computation of electromagnetic fields in accelerators, J. Comput. Phys. 207 (2005) 69]. It does not have dispersion in the longitudinal direction and the dispersion properties in the transverse plane are improved. The explicit character of the new scheme allows a uniformly stable conformal method without iterations and the scheme can be parallelized easily. It assures energy and charge conservation. A version of this explicit scheme for rotationally symmetric structures is free from the progressive time step reducing for higher order azimuthal modes as it takes place for Yee’s explicit method used in the most popular electrodynamics codes.     

柱面内爆磁通量压缩实验中的磁扩散过程

利用一维磁流体力学程序MC11D,对套筒材料为不锈钢的柱面内爆磁通量压缩实验进行了数值模拟,研究了其中的磁扩散过程。计算结果表明:当套筒空腔中的磁场被压缩到350 T左右时,峭面磁扩散波开始形成,磁扩散波的波前从套筒内壁开始以0.75 km/s的平均速度向外快速推进,给磁场的压缩带来了不利影响;随着套筒内壁温度迅速升高,内壁附近会形成一个电阻率仅有0.3 mcm左右的等离子体保护层,又极大地减缓了空腔磁场向套筒中扩散的速度。在磁压缩过程中,峭面磁扩散波和等离子体层对于空腔磁场的扩散起着相反的作用,两者在发展的过程中相互竞争,在不同的阶段分别起着主导作用。     

Magnetic helicity tensor for an anisotropic turbulence

The evolution of the magnetic helicity tensor for a nonzero mean magnetic field and for large magnetic Reynolds numbers in an anisotropic turbulence is studied. It is shown that the isotropic and anisotropic parts of the magnetic helicity tensor have different characteristic times of evolution. The time of variation of the isotropic part of the magnetic helicity tensor is much larger than the correlation time of the turbulent velocity field. The anisotropic part of the magnetic helicity tensor changes for the correlation time of the turbulent velocity field. The mean turbulent flux of the magnetic helicity is calculated as well. It is shown that even a small anisotropy of turbulence strongly modifies the flux of the magnetic helicity. It is demonstrated that the tensor of the magnetic part of the alpha effect for weakly inhomogeneous turbulence is determined only by the isotropic part of the magnetic helicity tensor.     

静止条件下轨道炮膛内磁场分布特性分析

为了分析轨道炮静止条件下膛内磁场分布特性, 建立了轨道炮二维计算模型, 基于磁扩散方程与安培定律, 得到导轨和电枢各区域电流密度值, 并通过毕奥-萨伐尔定律对轨道炮电枢前端各考察点磁通密度进行理论计算, 基于电磁感应法进行了膛内磁场测量实验, 实验测量值与理论计算值基本一致, 结果表明, 膛内磁场大小主要由流经电枢和导轨的的电流决定, 电枢前端中心轴线上各考察点, 随着与电枢前端面距离的增大, 磁通密度峰值呈衰减趋势, 但衰减速度逐渐变小。研究结果有助于轨道炮膛内强磁场屏蔽与智能弹药设计。     

漂移波湍流中“clumps”理论

本文基于Misguich和Balescu提出的轨道的随机处理发展了漂移波湍流中“clumps”的一种理论。指出clump效应不仅存在于非磁化湍性等离子体中也存在于磁化湍性等离子体中。它的存在使得实际横越磁场的扩散比Dupree理论预言的要小得多。导出了clumps寿命的一个明晰的表达式,它正比于横越磁场扩散的特征时间并对数地依赖于粒子的初始相对位置。 关键词：     

Time-Domain Numerical Solutions of Maxwell Interface Problems with Discontinuous Electromagnetic Waves

This paper is devoted to time domain numerical solutions of two-dimensional (2D) material interface problems governed by the transverse magnetic (TM) and transverse electric (TE) Maxwell's equations with discontinuous electromagnetic solutions. Due to the discontinuity in wave solutions across the interface, the usual numerical methods will converge slowly or even fail to converge. This calls for the development of advanced interface treatments for popular Maxwell solvers. We will investigate such interface treatments by considering two typical Maxwell solvers – one based on collocation formulation and the other based on Galerkin formulation. To restore the accuracy reduction of the collocation finite-difference time-domain (FDTD) algorithm near an interface, the physical jump conditions relating discontinuous wave solutions on both sides of the interface must be rigorously enforced. For this purpose, a novel matched interface and boundary (MIB) scheme is proposed in this work, in which new jump conditions are derived so that the discontinuous and staggered features of electric and magnetic field components can be accommodated. The resulting MIB time-domain (MIBTD) scheme satisfies the jump conditions locally and suppresses the staircase approximation errors completely over the Yee lattices. In the discontinuous Galerkin time-domain (DGTD) algorithm – a popular Galerkin Maxwell solver, a proper numerical flux can be designed to accurately capture the jumps in the electromagnetic waves across the interface and automatically preserves the discontinuity in the explicit time integration. The DGTD solution to Maxwell interface problems is explored in this work, by considering a nodal based high order discontinuous Galerkin method. In benchmark TM and TE tests with analytical solutions, both MIBTD and DGTD schemes achieve the second order of accuracy in solving circular interfaces. In comparison, the numerical convergence of the MIBTD method is slightly more uniform, while the DGTD method is more flexible and robust.     

电磁搅拌中旋转磁场及洛伦兹力的数值模拟

由于工程中应用广泛的电磁搅拌问题很难得到解析解,通过有限元软件ANSYS对其进行了数值求解。结果表明：旋转磁场在结晶器搅拌区域内产生电磁力,使钢液在水平方向形成旋转流动。随着频率的增加,磁感应强度逐渐减小、电磁力密度则先增加后减小。在频率一定的情况下,通电线圈电压的增加可导致电磁力密度的增大,通过相关物理理论可对其进行合理解释。     

Initial transient process in a simple helical flux compression generator

An analytical scheme on the initial transient process in a simple helical flux compression generator, which includes the distributions of both the magnetic field in the hollow of an armature and the conducting current density in the stator, is developed by means of a diffusion equation. A relationship between frequency of the conducting current, root of the characteristic function of Bessel equation and decay time in the armature is given. The skin depth in the helical stator is calculated and is compared with the approximate one which is widely used in the calculation of magnetic diffusion. Our analytical results are helpful to understanding the mechanism of the loss of magnetic flux in both the armature and stator and to suggesting an optimal design for improving performance of the helical flux compression generator.