多介质流体界面不稳定性程序

研制了二维多介质流体程序，主要包括单介质内高精度流体力学计算，多介质混合网格内各种介质输运过程和压力驰豫平衡过程计算、实际状态方程的黎曼解计算。流体计算分别采用高分辨两步PPM（Parabolic Piecewise Method）算法、TVD（Total Variation Diminishing）算法和FCT（Flux Corrected—Transport）算法，流体界面追踪采用VOF（Volume-of-Fluid）。数值求解可压缩多流体方程组和可压缩VOF方程。二维界面追踪分别采用一阶精度Youngs方法和二阶精度Elivira方法，三维界面追踪采用一阶精度Youngs方法，     

运动激波和气泡串相互作用的初步数值模拟

通过对激波和流体界面相互作用诱导的大变形界面演化的数值模拟,验证Level set方法精确模拟多个流体界面的有效性.采用2阶迎风TVD求解欧拉方程得到流场解,采用5阶WENO求解Level set方程追踪多流体界面,采用GFM方法处理流体内界面.利用文[1]的计算结果校核本文程序.在此基础上,对运动激波和气泡串相互作用过程进行了初步数值模拟,得到了不同时刻运动激波和圆管内的两个气泡作用后的演化图象,包括压力和密度等值线分布.计算结果表明:针对推广后的多界面Level set方程,该方法仍可高质量地捕捉多个流体界面.     

等离子体电极普克尔盒电光开关单脉冲过程数值模拟

采用流体模型对等离子体电极普克尔盒(PEPC)电光开关单脉冲过程进行了数值模拟分析.模型包括带电粒子连续性方程、动量守恒方程、电子平均能量方程及空间电位泊松方程.分别采用隐式指数差分格式，超松弛迭代法(SOR)和经典四阶龙格-库塔法(R-K)对带电粒子连续性方程，泊松方程和电子平均能量方程进行数值求解.模拟分析了PEPC单脉冲过程中的带电粒子浓度、电子温度、空间电场、PEPC的放电电流、晶体两侧电压和开关效率的时间演化特性.模型得出了PEPC中气体放电等离子体的微观物理过程与PEPC宏观参量的关系，对设计 关键词： 等离子体电极普克尔盒 电光开关 数值模拟 气体放电     

求解Navier-Stokes方程组的组合紧致迎风格式

给出一种新的至少有四阶精度的组合紧致迎风(CCU)格式,该格式有较高的逼近解率,利用该组合迎风格式,提出一种新的适合于在交错网格系统下求解Navier-Stokes方程组的高精度紧致差分投影算法.用组合紧致迎风格式离散对流项,粘性项、压力梯度项以及压力Poisson方程均采用四阶对称型紧致差分格式逼近,算法的整体精度不低于四阶.通过对Taylor涡列、对流占优扩散问题和双周期双剪切层流动问题的计算表明,该算法适合于对复杂流体流动问题的数值模拟.     

大雷诺数Navier-Stokes方程的两水平亚格子模型稳定化方法

基于两重网格离散方法,提出三种求解大雷诺数定常Navier-Stokes方程的两水平亚格子模型稳定化有限元算法.其基本思想是首先在一粗网格上求解带有亚格子模型稳定项的Navier-Stokes方程,然后在细网格上分别用三种不同的校正格式求解一个亚格子模型稳定化的线性问题,以校正粗网格解.通过适当的稳定化参数和粗细网格尺寸的选取,这些算法能取得最优渐近收敛阶的有限元解.最后,用数值模拟验证三种算法的有效性.     

求解含有高阶导数偏微分方程的局部间断Petrov-Galerkin方法

构造一类求解三种类型偏微分方程的间断Petrov-Galerkin方法.求解的方程分别含有二阶、三阶和四阶偏导数,包括Burgers型方程、KdV型方程和双调和型方程.首先将高阶微分方程转化成为与之等价的一阶微分方程组,再将求解双曲守恒律的间断Petrov-Galerkin方法用于求解微分方程组.该方法具有四阶精度且具有间断Petrov-Galerkin方法的优点.数值实验表明该方法可以达到最优收敛阶而且可以模拟复杂波形相互作用,如孤立子的传播及相互碰撞等.     

求解含有高阶导数偏微分方程的局部间断Petrov-Galerkin方法（英文）

构造一类求解三种类型偏微分方程的间断Petrov-Galerkin方法.求解的方程分别含有二阶、三阶和四阶偏导数,包括Burgers型方程、KdV型方程和双调和型方程.首先将高阶微分方程转化成为与之等价的一阶微分方程组,再将求解双曲守恒律的间断Petrov-Galerkin方法用于求解微分方程组.该方法具有四阶精度且具有间断Petrov-Galerkin方法的优点.数值实验表明该方法可以达到最优收敛阶而且可以模拟复杂波形相互作用,如孤立子的传播及相互碰撞等.     

耦合广义非线性薛定谔方程的相互作用表象龙格库塔算法及其误差分析

本文通过表象变换, 将耦合广义非线性薛定谔方程 (C-GNLSE) 变换成相互作用表象中的向量方程, 再利用向量形式的4阶龙格-库塔迭代格式, 建立了一种在频域内求解C-GNLSE的同步更新迭代算法. 通过将该向量形式的相互作用表象中的4阶龙格-库塔 (V-JH-RK4IP) 算法应用于高双折射光子晶体光纤中超连续谱产生的数值模拟, 验证了算法的有效性, 通过与现有其他典型算法的比较, 表明以V-JH-RK4IP算法求解C-GNLSE具有最高的计算精度和计算效率. 关键词： 耦合广义非线性薛定谔方程(C-GNLSE) 相互作用表象 4阶龙格-库塔算法 超连续谱产生     

聚合物充填过程中裹气现象的数值模拟

针对聚合物充填过程中的裹气现象,采用一种有限元（FEM）-间断有限元（DG）耦合算法对其进行数值模拟。对于自由运动界面,采用水平集（Level Set）方法进行捕捉;用XPP（eXtended Pom-Pom）本构模型来描述黏弹性流体的流变行为。采用有限元-间断有限元耦合算法求解统一的流场方程,并采用隐式间断有限元求解XPP本构方程、Level Set及其重新初始化方程。数值结果与文献中的实验结果及模拟结果吻合较好,验证了数值方法的稳定性及准确性。分析带有非规则嵌件型腔内,注射速度及浇口尺寸对裹气现象的影响,裹气容易出现在较高注射速度及较小浇口的情形。     

Rayleigh-Taylor和Richtmyer-Meshkov不稳定性的FCT方法数值模拟

介绍了二维流体力学不稳定性程序的FCT数值方法,数值模拟Rayleigh-Taylor和Richt-myer-Meshkov流体不稳定性,在线性阶段,与线性理论符合很好;在非线性阶段,与俄罗斯激波管实验的计算结果符合很好。计算结果表明:FCT方法有较高计算精度,给出了不稳定性发展的好的图象,适合于ICF烧蚀和内爆流体不稳定性问题的计算。     

均匀电场SF6短气隙放电过程动态模拟

根据基本物理定律和流体力学,构建均匀电场下SF₆短气隙放电流体模型,运用通量校正传输法(flux-corrected transport)数值分析大气压下4 mm间隙SF₆的放电过程,展现放电空间带电粒子产生、复合、附着、扩散以及光致电离动态过程,获得了放电间隙电场畸变、带电粒子动力学行为和放电通道形成发展历程和时空分布,根据R-M判据求出模型放电过程中电子崩转向流注的时空临界点,印证了光致电离在流注发展阶段的重要作用.     

Flux-corrected transport. III. Minimal-error FCT algorithms

This paper presents an error analysis of numerical algorithms for solving the convective continuity equation using flux-corrected transport (FCT) techniques. The nature of numerical errors in Eulerian finite-difference solutions to the continuity equation is analyzed. The properties and intrinsic errors of an “optimal” algorithm are discussed and a flux-corrected form of such an algorithm is demonstrated for a restricted class of problems. This optimal FCT algorithm is applied to a model test problem and the error is monitored for comparison with more generally applicable algorithms. Several improved FCT algorithms are developed and judged against both standard flux-uncorrected transport algorithms and the optimal algorithm. These improved FCT algorithms are found to be four to eight times more accurate than standard non-FCT algorithms, nearly twice as accurate as the original SHASTA FCT algorithm, and approach the accuracy of the optimal algorithm.     

Learning-based structurally-guided construction of resting-state functional correlation tensors

Functional magnetic resonance imaging (fMRI) measures changes in blood-oxygenation-level-dependent (BOLD) signals to detect brain activities. It has been recently reported that the spatial correlation patterns of resting-state BOLD signals in the white matter (WM) also give WM information often measured by diffusion tensor imaging (DTI). These correlation patterns can be captured using functional correlation tensor (FCT), which is analogous to the diffusion tensor (DT) obtained from DTI. In this paper, we propose a noise-robust FCT method aiming at further improving its quality, and making it eligible for further neuroscience study. The novel FCT estimation method consists of three major steps: First, we estimate the initial FCT using a patch-based approach for BOLD signal correlation to improve the noise robustness. Second, by utilizing the relationship between functional and diffusion data, we employ a regression forest model to learn the mapping between the initial FCTs and the corresponding DTs using the training data. The learned forest can then be applied to predict the DTI-like tensors given the initial FCTs from the testing fMRI data. Third, we re-estimate the enhanced FCT by utilizing the DTI-like tensors as a feedback guidance to further improve FCT computation. We have demonstrated the utility of our enhanced FCTs in Alzheimer's disease (AD) diagnosis by identifying mild cognitive impairment (MCI) patients from normal subjects.     

Structure of tetragonal martensite in the In<Subscript>95.42</Subscript>Cd<Subscript>4.58</Subscript> cast alloy

The structure of martensite in the In_95.42Cd_4.58 alloy has been studied by metallography, X-ray diffraction, dilatometry, and transmission electron microscopy. It has been shown that a massive structure built of colonies of tetragonal lamellar plates divided by a twin boundary {101}FCT is formed in the alloy under cooling below the martensite FCC → FCT transition temperature. The alloy recrystallizes after a cycle of FCT → FCC → FCT transitions with a decrease in the grain size by several times compared with the initial structure such fashion that the size of massifs and individual martensite lamella in the massif correlates with the change in the size of the alloy grain. Using thermal cycling, it has been revealed that the alloy tends to stabilize the high-temperature phase.     

A geometrically-conservative,synchronized, flux-corrected remap for arbitrary Lagrangian–Eulerian computations with nodal finite elements

This article describes a conservative synchronized remap algorithm applicable to arbitrary Lagrangian–Eulerian computations with nodal finite elements. In the proposed approach, ideas derived from flux-corrected transport (FCT) methods are extended to conservative remap. Unique to the proposed method is the direct incorporation of the geometric conservation law (GCL) in the resulting numerical scheme. It is shown here that the geometric conservation law allows the method to inherit the positivity preserving and local extrema diminishing (LED) properties typical of FCT schemes. The proposed framework is extended to the systems of equations that typically arise in meteorological and compressible flow computations. The proposed algorithm remaps the vector fields associated with these problems by means of a synchronized strategy. The present paper also complements and extends the work of the second author on nodal-based methods for shock hydrodynamics, delivering a fully integrated suite of Lagrangian/remap algorithms for computations of compressible materials under extreme load conditions. Extensive testing in one, two, and three dimensions shows that the method is robust and accurate under typical computational scenarios.     

Reversible and irreversible martensitic transformations in Fe-Pd and Fe-Pd-Co alloys

Ferromagnetic Fe-Pd shape memory alloys (SMA) undergo a martensitic phase transformation during cooling from a parent FCC phase to a tetragonal FCT martensite. This transformation is thermoelastic and reversible giving rise to the shape memory effect. On further cooling an irreversible FCT to BCT transformation occurs that makes impossible the memory effect. Nevertheless, the transformation from reversible to irreversible phase has been not complete since a volume fraction of reversible phase in the alloy is retained even after cooling below the temperature of appearance of the irreversible phase. The addition of Co lowers the temperature of the reversible and irreversible phase transformations but also reduces the amount of transformed irreversible martensite after cooling to 10 K.     

Failsafe flux limiting and constrained data projections for equations of gas dynamics

A new approach to flux limiting for systems of conservation laws is presented. The Galerkin finite element discretization/L² projection is equipped with a failsafe mechanism that prevents the birth and growth of spurious local extrema. Within the framework of a synchronized flux-corrected transport (FCT) algorithm, the velocity and pressure fields are constrained using node-by-node transformations from the conservative to the primitive variables. An additional correction step is included to ensure that all the quantities of interest (density, velocity, pressure) are bounded by the physically admissible low-order values. The result is a conservative and bounded scheme with low numerical diffusion. The new failsafe FCT limiter is integrated into a high-resolution finite element scheme for the Euler equations of gas dynamics. Also, bounded L² projection operators for conservative interpolation/initialization are designed. The performance of the proposed limiting strategy and the need for a posteriori control of flux-corrected solutions are illustrated by numerical examples.     

An evaluation of the FCT method for high-speed flows on structured overlapping grids

This study considers the development and assessment of a flux-corrected transport (FCT) algorithm for simulating high-speed flows on structured overlapping grids. This class of algorithm shows promise for solving some difficult highly-nonlinear problems where robustness and control of certain features, such as maintaining positive densities, is important. Complex, possibly moving, geometry is treated through the use of structured overlapping grids. Adaptive mesh refinement (AMR) is employed to ensure sharp resolution of discontinuities in an efficient manner. Improvements to the FCT algorithm are proposed for the treatment of strong rarefaction waves as well as rarefaction waves containing a sonic point. Simulation results are obtained for a set of test problems and the convergence characteristics are demonstrated and compared to a high-resolution Godunov method. The problems considered are an isolated shock, an isolated contact, a modified Sod shock tube problem, a two-shock Riemann problem, the Shu–Osher test problem, shock impingement on single cylinder, and irregular Mach reflection of a strong shock striking an inclined plane.     

3-D numerical analysis of EHD turbulent flow and mono-disperse charged particle transport and collection in a wire-plate ESP

The present study attempts to develop a detailed numerical approach and a simulation procedure to predict the motion of gas, ions and particles inside a simple parallel plate channel containing a single corona wire. A hybrid Finite Element (FEM)-Flux Corrected Transport (FCT)-Finite Volume (FVM) method is used: the FEM–FCT numerical algorithm is applied for modeling the steady-state corona discharge, while the turbulent gas flow and the particle motion under electrostatic forces are modeled using the commercial CFD code FLUENT. Calculations for the gas flow are carried out by solving the Reynolds-averaged Navier–Stokes equations and turbulence is modeled using the k–? turbulence model. An additional source term is added to the gas flow equation to include the effect of the electric field, obtained by solving a coupled system of the electric field and charge transport equations using User-Defined Functions (UDFs). The particle phase is simulated based on the Lagrangian approach, where a large number of particles is traced with their motion affected by the gas flow and electrostatic forces using the Discrete Phase Model (DPM) in FLUENT. The developed model is useful to gain insight into the particle collection phenomena that take place inside an ESP.