二维三温辐射扩散方程组两层预条件子的自适应求解

针对实际应用中若干典型三温线性系统,分析求解二维三温辐射扩散方程离散线性系统的代数两层预条件子(PCTL)的算法效率.结果表明,PCTL的算法效率与三个温度之间的耦合强度以及单温子系统对角占优性强弱程度有很大关系.为此,通过刻画三温线性系统的耦合强度和单温子系统对角占优性特征,提出一种PCTL中子系统的自适应求解算法.数值结果表明,可以显著改善PCTL的算法效率.对于实际数值模拟应用中37个典型三温线性系统,相对于经典AMG算法,算法整体加速2.5倍.数值实验表明算法具有很强的鲁棒性.     

三温能量方程离散线性系统的两层迭代算法收敛因子估计及特征分析

基于代数多重网格(AMG)方法的理论框架,详细分析基于物理量粗化的两层迭代方法(PCTL)算法的具体收敛性质,刻画算法收敛因子的合理上界,为PCTL算法提供理论保证。进一步深入分析影响PCTL算法收敛速度的代数特征,如对角占优性和耦合强度,为PCTL算法的应用和算法调优提供了理论指导。     

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。     

并行代数多重网格算法可扩展性能分析

对当今求解大型稀疏线性代数方程组最有效的迭代方法之--代数多重网格(AMG)算法的并行计算进行可扩展性能分析.给出一套并行计算可扩展性能分析方法,用于分析和指导并行迭代算法及实现技术的设计与优化并应用于并行AMG算法.分析表明,网格算子的平均模式大小和迭代过程的算法效率分别制约了AMG算法启动阶段和迭代求解阶段并行性能的发挥,成为该类算法急需解决的两个关键问题.     

隐-显积分因子间断Galerkin方法求解二维辐射扩散方程

提出一种求解二维非平衡辐射扩散方程的数值方法.空间离散上采用加权间断Galerkin有限元方法,其中数值流量的构造采用一种新的加权平均;时间离散上采用隐-显积分因子方法,将扩散系数线性化,然后用积分因子方法求解间断Galerkin方法离散后的非线性常微分方程组.数值试验中在非结构网格上求解了多介质的辐射扩散方程.结果表明:对于强非线性和强耦合的非线性扩散方程组,该方法是一种非常有效的数值算法.     

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.     

半导体器件数值模拟中电子连续性方程的求解算法

针对电子连续性方程的离散代数方程组,对离散线性系统的矩阵进行分析,得到矩阵的三类特点;针对大规模电子连续性方程的离散方程组,采用预处理Krylov子空间方法进行求解,并比较和分析几类预处理方法的效果。结果表明：代数多重网格(AMG)预处理Krylov子空间方法在求解离散电子连续性方程方面非常有效。开展AMG预处理Krylov子空间方法求解离散电子连续性方程的大规模并行可扩展性测试,比较和分析了AMG方法中三类关键算法参数的选取。     

用代数多重网格法求解一维分裂格式的Euler方程

提出了代数多重网格法(AMG)的一种新算法。新算法改进了插值公式和粗网格方程,并把它应用到求解一维的分裂格式Euler方程。数值结果表明,对于具有高CFL条件数的Euler方程,代数多重网格法可以求解;对于Gaus-Seidel方法求解不能收敛的代数方程组,代数多重网格法求解可以收敛。新算法改进了代数多重网格法的收敛性和扩展了它的应用范围,数值结果表明了它的有效性和强壮性。     

节块内嵌离散纵标(SN)方法的算法研究及程序开发

介绍节块内嵌离散纵标(S_N)方法求解三维堆芯中子输运/扩散方程的算法框架.在基于扩散理论的三维粗网节块展开方法(NEM)的算法体系中,用基于输运理论的径向二维细网节块离散纵标方法(NDOM)的内迭代过程,替代节块展开方法(NEM)内迭代的径向求解过程.该算法充分考虑了核电厂反应堆堆芯的三维结构特点,另一方面,也充分利用了已经成熟的三维粗网节块展开方法(NEM)和二维离散纵标方法(S_N)的研究成果,同时有效避免了利用离散纵标方法(S_N)求解三维中子输运方程所面临的计算内存和计算时间的瓶颈问题.编制开发二维多群节块离散纵标方法(NDOM)模块程序NS_NM和三维多群节块展开方法(NEM)模块程序MGNEM,并以此为基础编制开发节块内嵌S_N方法的模块程序HANWIND;其中,NS_NM为HANWIND求解两维问题的功能模块.针对OECD/NEA-2D C5G7MOX基准问题以及两环路核电厂三维堆芯的数值验算结果表明,节块内嵌S_N方法的算法开发及程序编制有效、切实可行.     

二维三温辐射流体力学拉氏计算中的子网格压力方法

研究对应于电子压、离子压、光子压的扰动隅角力的计算方法,提出二维三温辐射流体力学拉氏计算中的两种子网格压力方法,即基于状态方程和基于几何的方法.数值试验表明,这两种方法均能很好地抑制二维三温辐射流体力学拉氏计算中出现的网格非物理畸变.     

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从Lagrange观点出发,采用分裂格式法求解一维辐射流体力学方程组中的三温方程,用于紧凑等离子体环与靶碰撞产生的X射线辐射的数值模拟研究。提出了求解电子、离子、辐射场三温相脱离的能量方程的隐式差分格式,介绍了能量交换项与压力做功及热传导项分开计算的分裂格式方法,数值模拟得到了其对温度变化的影响。     

基于热峰模型的单粒子效应模拟研究

单粒子效应是航天电子器件失效的重要原因,研究其物理过程对航天电子器件寿命预测、器件抗辐照加固有着重要的意义。现有的模型多从线性能量沉积的角度来解释单粒子翻转,因此无法解释单粒子效应地面实验模拟过程中的温度效应。建立了一个新模型,从高能带电离子与材料相互作用的物理过程出发,通过解三维的热扩散方程,计算出能量在材料中沉积、交换、扩散,得到电子和晶格温度的空间分布以及时间演化过程。推断出离子辐照过程中导致的自由电子浓度和收集电荷随LET的变化关系。此模型解释了单粒子效应中随着器件温度升高,单粒子效应截面增加的现象。     

光子与相对论麦克斯韦分布电子散射截面的蒙特卡罗计算方法

高温全电离等离子体的辐射输运问题中,光子与电子的Compton散射与逆Compton散射是其中重要的特性,光子与相对论麦克斯韦电子散射的描述及截面的计算非常复杂且费时.本文提出了一种用于模拟计算光子与相对论麦克斯韦速度分布电子散射截面的蒙特卡罗计算方法.给出了各步骤的具体实现办法,推导了对应的计算公式,研究了相对论电子速率抽样方法,编写了光子与相对论电子散射的微观截面的蒙特卡罗计算程序.开展了高温全电离等离子体中,不同能量光子与不同温度电子散射的微观散射截面计算和分析.模拟计算结果显示,在电子温度低于25 keV情况下,本文方法与多重数值积分方法的计算结果非常接近;但随着电子温度继续升高,二者差异逐渐增大并较明显,经分析,可能是本文方法目前的电子速率抽样偏差所致,希望将来能够找到更好的相对论电子速率抽样方法以克服此缺陷.     

高温稠密气态混合物质压强的计算

 基于含温有界相对论自洽场平均原子模型,计算了高温稠密条件下气态混合物的压强。通过求解相对论Dirac方程给出有界原子的电子波函数和轨道能量。电子在各单电子轨道上的平均占据数服从Fermi-Dirac分布。以铝、铝镁混合物、铁和高能炸药HMX（奥克托金）为算例,计算了在一些温度密度点下的压强并给出了分析。     

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.     

Does femtosecond time-resolved second-harmonic generation probe electron temperatures at surfaces?

Femtosecond pump-probe second-harmonic generation (SHG) and transient linear reflectivity measurements were carried out on polycrystalline Cu, Ag and An in air to analyze whether the electron temperature affects Fresnel factors or nonlinear susceptibilities, or both. Sensitivity to electron temperatures was attained by using photon energies near the interband transition threshold. We find that the nonlinear susceptibility carries the electron temperature dependence in case of Ag and Au, while for Cu the dependence is in the Fresnel factors. This contrasting behavior emphasizes that SHG is nota priori sensitive to electron dynamics at surfaces or interfaces, notwithstanding its cause.     

Room temperature intra-band lasing in quantum dot arrays placed in high photon density cavities—a theoretical study

Intersubband (intra-band) transitions are very attractive forlong wavelength lasers due to the high degree of tailoring possible in the emission spectra. In general, if intra-band population inversion is to be created in a conduction band quantum well by carrier injection at the barrier energy, it is necessary that the electron non-radiative intra-band energy relaxation times are long. Additionally, the extraction time for the electron from the lower state should be short. In a bipolar device studied here, this means the bandedge electron-hole recombination times should be short.The use of sub-two-dimensional (2D) structures (quantum dots) allows us to increase the intra-band energy relaxation time from about a picosecond for bulk or quasi-2D systems to several hundred picoseconds at room temperatures. Also, by placing these structures in a cavity with a high photon number, it is possible to decrease the bandedge electron-hole recombination times through stimulated emission. Our studies show that strong population inversion and lasing under d.c. conditions is possible at room temperature in such systems.     

Electron temperature diagnostics of aluminium plasma in a z-pinch experiment at the ＂QiangGuang-1＂ facility

<正>Two curved crystal spectrometers are set up on the "QiangGuang-1" generator to measure the z-pinch plasma spectra emitted from planar aluminum wire array loads.Kodak Biomax-MS film and an IRD AXUVHS5# array are employed to record time-integrated and time-resolved free-bound radiation,respectively.The photon energy recorded by each detector is ascertained by using the L-shell lines of molybdenum plasma.Based on the exponential relation between the continuum power and photon energies,the aluminum plasma electron temperatures are measured.For the time-integrated diagnosis,several "bright spots" indicate electron temperatures between(450 eV～520 eV)±35%.And for the time-resolved ones,the result shows that the electron temperature reaches about 800 eV±30%at peak power. The system satisfies the demand of z-pinch plasma electron temperature diagnosis on a～1 MA facility.     

Unified System of Differential Equations for Plasmas and Boundary Layers

Starting from the Boltzmann equation the moment equations up to the third order for a non-quasineutral plasma are derived. It is shown that for a non-quasineutral plasma, in the distinction from the second order set of moment equations, the systems of the first order and of the third order can be closed in a physically reasonable manner by a relatively simple method when near the walls the ion gas has a high drift velocity caused by an electric field. From this follows that in non-quasineutral plasmas the ion pressure must be neglected in the first order set of equations consisting of the equations of continuity and of momentum transfer. Terms of the first order in the ion pressure related to the electron pressure are taken into consideration for the third order system. In this way one obtains a unified set of differential equations to treat both the quasineutral plasma core and the space charge sheath at the walls jointly taking into account a non-vanishing ion temperature. This set of equations is applied to the positive column in the free-fall regime.