二维多介质流体自适应网格技术应用

自适应网格技术能够对复杂几何形状的流场以及大变形问题进行数值模拟，特别是能够很好地捕捉几何尺度较小、物理量空间变化梯度大的强间断，如激波。该方法在初始网格基础上根据物形特点或流场特点在局部区域内不断进行网格细化，实现精度符合要求、分布合理且经济有效的一种网格技术。     

移动网格方法求解二维流体力学方程组

移动网格方法是求解发展方程的一种方法，它根据物理解的变化，随时调整网格的疏密。在流体力学问题中，由于激波、接触间断等变化剧烈的区域在全流场中只占很小一部分，使用移动网格方法可以在不减少计算精度的情况下，较大地减少计算量。     

ρ-VOF:一种可清晰模拟自由界面的两相流方法

文章通过对EFM(effective field modeling)模型进行简化, 消除了原模型的非守恒性项和非双曲性特性项, 发展了一种基于密度的气液两相流模拟方法: ρ-VOF方法.利用体积分数信息对控制单元内的自由界面进行重构, 得到了控制单元内流体的空间分布, 并采用AUSM+-up格式获得考虑气液流体接触间断信息的对流通量.新方法可统一处理激波间断和接触间断的相互作用, 保持自由界面的尖锐性, 并且其计算量与自由界面的空间复杂度无关.最后, 数值模拟了液体激波管气液激波管和气体激波跨二维液滴传播等问题, 并与文献结果进行对比, 验证了本方法在气液两相流模拟中的准确性.      

基于特征线理论的辨识法在激波装配中的应用

准确地给出激波位置信息对于激波装配极为重要.但是,在使用计算流体力学（computational fluid dyna-mics,CFD）方法模拟复杂流动时很难准确地给出激波的位置.根据激波捕捉得到的流场信息确定的激波位置往往带有极大误差,在定常问题的模拟中,这种误差可以随着迭代逐渐消除,然而在非定常问题的模拟中,这种误差往往会积累甚至导致计算崩溃.文章将基于特征线理论的激波辨识技术应用到激波装配中,根据已有流场信息准确判断激波的位置.对于定常问题,该方法的应用加速了收敛速度;对于非定常问题,该方法的应用可以极大地避免初始误差的产生.      

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.     

弹塑性流体力学拉氏自适应网格和网格重分守恒重映数值模拟方法

拉氏自适应重分弹塑性流体力学有限元程序实现了网格完全自适应，具有良好、灵活的非结构自适应网格数据结构，实现了滑移界面两边(接触间断)网格动态调整，网格的细分和合并处理灵活，网格重分和网格自适应模块兼容、守恒重映，网格重分中采用多种方法控制新网格的质量，爆轰计算可采用Lee-Tarver的化学反应率模式。初步数值计算结果表明，弹塑性流体力学拉氏自适应重分数值模拟方法合理，计算结果正确，基本反映了流场的物理结构。     

多介质五方程简化模型及界面捕捉的人工压缩算法

根据两介质五方程简化模型的基本假设,发展了适用于任意多种介质的体积分数方程。为了捕捉多介质界面,将HLLC-HLLCM混合型数值通量的计算格式推广应用于二维平面和柱几何的多介质复杂流动问题,在高阶精度的数据重构过程中采用斜率修正型人工压缩方法ACM。通过一维、二维多介质黎曼问题算例测试,结果表明：发展的计算格式能够较好地分辨接触间断和激波,间断附近物理量无振荡;对于添加了初始扰动的激波问题,能够有效抑制激波数值不稳定性;使用二维柱球SOD问题和接触间断型黎曼问题检验计算格式对多介质复杂流动问题的适应性。     

流动变量线性分布的MUSCL格式

本文提出一种线性函数斜率的确定方法并证明用其近似代替网格内流动变量的初始分布,MUSCL格式具有二阶精度。引入单调性限制条件和一定的耗散机制后,该方法适合于Euler坐标系下的计算。本文在处理间断时,用激波关系式代替特征线方程,解决了特征线法在全流场计算中的应用问题。最后,本文给出Emery问题和一个火箭喷流问题的计算结果。     

面向高超声速飞行器的激波智能预测方法

高超声速飞行器激波位置的准确预测能够有效提升数值模拟的精度和效率。一方面, 对高超声速飞行器激波附近网格进行正交和加密处理, 可有效提升数值计算精度; 另一方面, 使用高超声速飞行器激波位置对计算网格进行修正, 能够加速CFD计算收敛过程。提出了一种基于机器学习的高超声速飞行器激波智能预测方法, 对典型高超声速飞行器外形进行激波位置的高效准确预测。首先, 针对典型高超声速飞行器外形和典型飞行状态, 使用数值模拟方法获得收敛的流场, 并采用基于Mach数等值线的激波提取方法, 从流场中判别激波面并提取构成激波面的关键点位置, 形成训练数据; 然后采用有监督学习算法, 学习关键点位置, 并利用二次曲线沿流向拟合关键点形成初步的激波线族; 最后, 基于剖面压力云图, 构造基于投影压力图像的智能预测神经网络, 对初步形成的激波线族进行修正, 并获得三维激波面。大量的实验结果表明, 激波预测模型能够对高超声速飞行器激波位置做出准确预测, 预测的激波面与CFD数值计算结果中提取的激波面误差在10-4量级。      

含有大位移动边界的复杂流场的数值模拟

含有运动弹丸的膛口流场是典型的大位移动边界问题,同时弹丸在出膛过程中,流场的结构也会发生变化,增加了流场的复杂程度.在对该流场的数值模拟中,将它分为两个区:弹丸运动区和普通流场区,它们之间用一个特殊的分区边界联系,同时运用网格局部重构技术处理弹丸运动造成的网格变形问题,并将对称轴定义为网格变形边界,使得弹丸在对称轴上运动过程中不会导致对称轴上的网格体积为负.从计算结果可以看出整个膛口波系结构变化过程和弹丸先加速后减速的过程,从而表明该动网格处理方法是成功的.     

基于LU-SGS的非结构弹簧网格迭代算法

针对运动间断拟合中需频繁更新网格点位置的特点,提出一种基于LU-SGS(lower-upper symmetricGauss-Seidel)迭代方法的非结构弹簧网格运动算法.根据弹簧网格原理构建与网格拓扑关系相对应的稀疏系数矩阵,将LU-SGS思想成功引入动网格迭代算法,并辅以合理的网格运动管理策略,实现动网格的快速迭代.研究表明,在非结构网格下,LU-SGS算法可以满足运动间断拟合的需求,在流场隐式时间推进时,仍能保证获得稳定解;与传统的SOR方法相比,计算时耗减少20%以上.     

守恒律方程组的大时间步长叠波格式

大时间步长叠波格式最初思想为LeVeque提出的大时间步长Godunov格式,通过叠加间断分解发出的强波来构造数值格式.原方法只给出了间断强波的穿越叠加方法,文章对其进行了完善,并推广到多维.针对膨胀波提出了一种网格单元分解法可以自动满足熵条件,避免出现非物理解.给出了格式的具体计算公式,并用单个守恒律方程、一维/多维Euler方程组进行了数值计算.计算结果表明,新格式除了可以采用大时间步长的优点外,在一定范围内随CFL数增加其耗散反而更低,因而对激波接触间断膨胀波的分辨率更高.     

Nonlinear spectral-like schemes for hybrid schemes

In spectral-like resolution-WENO hybrid schemes,if the switch function takes more grid points as discontinuity points,the WENO scheme is often turned on,and the numerical solutions may be too dissipative.Conversely,if the switch function takes less grid points as discontinuity points,the hybrid schemes usually are found to produce oscillatory solutions or just to be unstable.Even if the switch function takes less grid points as discontinuity points,the final hybrid scheme is inclined to be more stable,provided the spectral-like resolution scheme in the hybrid scheme has moderate shock-capturing capability.Following this idea,we propose nonlinear spectral-like schemes named weighted group velocity control(WGVC)schemes.These schemes show not only high-resolution for short waves but also moderate shock capturing capability.Then a new class of hybrid schemes is designed in which the WGVC scheme is used in smooth regions and the WENO scheme is used to capture discontinuities.These hybrid schemes show good resolution for small-scales structures and fine shock-capturing capabilities while the switch function takes less grid points as discontinuity points.The seven-order WGVC-WENO scheme has also been applied successfully to the direct numerical simulation of oblique shock wave-turbulent boundary layer interaction.     

A model for the initiation of reaction sites during the uranium–hydrogen reaction assuming enhanced hydrogen transport through linear oxide discontinuities

A model for the initiation of hydride sites on uranium metal is described for hydride attack in the region of linear discontinuities in the surface oxide film. The model considers the effect of variations in hydrogen permeation through such discontinuities due to intrinsic oxide and metal parameters and operational variables. Expressions are derived for the time dependence of the hydrogen concentration in the metal and the maximum attained hydrogen concentration in terms of these parameters. The derived expressions therefore relate hydride precipitation time in the metal underlying any oxide discontinuity to the physical width of the discontinuity, its length, the hydrogen diffusion coefficient down the oxide discontinuity, the hydrogen diffusion coefficient in the underlying metal lattice and the hydrogen concentration in the oxide discontinuity at the gas-oxide interface. The model can therefore account for how changes in operational conditions such as hydrogen pressure may change hydride attack times in the region of such oxide discontinuities. The model can also explain why, after any given time, hydride attack may occur at some but not all of the oxide discontinuities surrounding any individual metal grain. The model also considers how hydride attack times may, or may not, be modified by the intersection of linear discontinuities in the surface oxide film. Finally, the model is able to explain the reported experimental observation that oxide discontinuities having only a short rather than a long length are less preferred sites of hydride attack.     

A direct-forcing embedded-boundary method with adaptive mesh refinement for fluid–structure interaction problems

In the present work we developed a structured adaptive mesh refinement (S-AMR) strategy for fluid–structure interaction problems in laminar and turbulent incompressible flows. The computational grid consists of a number of nested grid blocks at different refinement levels. The coarsest grid blocks always cover the entire computational domain, and local refinement is achieved by the bisection of selected blocks in every coordinate direction. The grid topology and data-structure is managed using the Paramesh toolkit. The filtered Navier–Stokes equations for incompressible flow are advanced in time using an explicit second-order projection scheme, where all spatial derivatives are approximated using second-order central differences on a staggered grid. For transitional and turbulent flow regimes the large-eddy simulation (LES) approach is used, where special attention is paid on the discontinuities introduced by the local refinement. For all the fluid–structure interaction problems reported in this study the complete set of equations governing the dynamics of the flow and the structure are simultaneously advanced in time using a predictor–corrector strategy. An embedded-boundary method is utilized to enforce the boundary conditions on a complex moving body which is not aligned with the grid lines. Several examples of increasing complexity are given to demonstrate the robustness and accuracy of the proposed formulation.     

A second order virtual node method for elliptic problems with interfaces and irregular domains

We present a second order accurate, geometrically flexible and easy to implement method for solving the variable coefficient Poisson equation with interfacial discontinuities or on irregular domains, handling both cases with the same approach. We discretize the equations using an embedded approach on a uniform Cartesian grid employing virtual nodes at interfaces and boundaries. A variational method is used to define numerical stencils near these special virtual nodes and a Lagrange multiplier approach is used to enforce jump conditions and Dirichlet boundary conditions. Our combination of these two aspects yields a symmetric positive definite discretization. In the general case, we obtain the standard 5-point stencil away from the interface. For the specific case of interface problems with continuous coefficients, we present a discontinuity removal technique that admits use of the standard 5-point finite difference stencil everywhere in the domain. Numerical experiments indicate second order accuracy in L^∞.     

A new electrical to mechanical coupling effect for nonlinear piezoelectric solids

A new electrical to mechanical coupling mechanism is identified whereby electric field rates across discontinuities in strain are shown to induce strain gradients across the discontinuity.     

Sources of spurious force oscillations from an immersed boundary method for moving-body problems

When a discrete-forcing immersed boundary method is applied to moving-body problems, it produces spurious force oscillations on a solid body. In the present study, we identify two sources of these force oscillations. One source is from the spatial discontinuity in the pressure across the immersed boundary when a grid point located inside a solid body becomes that of fluid with a body motion. The addition of mass source/sink together with momentum forcing proposed by Kim et al. [J. Kim, D. Kim, H. Choi, An immersed-boundary finite volume method for simulations of flow in complex geometries, Journal of Computational Physics 171 (2001) 132–150] reduces the spurious force oscillations by alleviating this pressure discontinuity. The other source is from the temporal discontinuity in the velocity at the grid points where fluid becomes solid with a body motion. The magnitude of velocity discontinuity decreases with decreasing the grid spacing near the immersed boundary. Four moving-body problems are simulated by varying the grid spacing at a fixed computational time step and at a constant CFL number, respectively. It is found that the spurious force oscillations decrease with decreasing the grid spacing and increasing the computational time step size, but they depend more on the grid spacing than on the computational time step size.     

Auditory discontinuities interact with categorization: implications for speech perception

Behavioral experiments with infants, adults, and nonhuman animals converge with neurophysiological findings to suggest that there is a discontinuity in auditory processing of stimulus components differing in onset time by about 20 ms. This discontinuity has been implicated as a basis for boundaries between speech categories distinguished by voice onset time (VOT). Here, it is investigated how this discontinuity interacts with the learning of novel perceptual categories. Adult listeners were trained to categorize nonspeech stimuli that mimicked certain temporal properties of VOT stimuli. One group of listeners learned categories with a boundary coincident with the perceptual discontinuity. Another group learned categories defined such that the perceptual discontinuity fell within a category. Listeners in the latter group required significantly more experience to reach criterion categorization performance. Evidence of interactions between the perceptual discontinuity and the learned categories extended to generalization tests as well. It has been hypothesized that languages make use of perceptual discontinuities to promote distinctiveness among sounds within a language inventory. The present data suggest that discontinuities interact with category learning. As such, "learnability" may play a predictive role in selection of language sound inventories.     

Initial conditions in non-equilibrium statistical mechanics: I. The generation of solitary waves from discontinuities

Using an iterative projection technique method, a time-evolution equation is derived for the single-particle distribution function. An initial condition with built-in temperature and density discontinuities is used. It is shown that four soliton pairs traveling from the discontinuities may be generated. For the case of a density discontinuity alone, the classical shock tube result is recovered. It is also shown that with a temperature discontinuity, such as may be found in two metals which are brought together, it is possible to generate charged solitary pulses, in addition to the expected flow of electrons across the boundary.