Mechanisms for the convergence of time-parallelized,parareal turbulent plasma simulations

Parareal is a recent algorithm able to parallelize the time dimension in spite of its sequential nature. It has been applied to several linear and nonlinear problems and, very recently, to a simulation of fully-developed, two-dimensional drift wave turbulence. The mere fact that parareal works in such a turbulent regime is in itself somewhat unexpected, due to the characteristic sensitivity of turbulence to any change in initial conditions. This fundamental property of any turbulent system should render the iterative correction procedure characteristic of the parareal method inoperative, but this seems not to be the case. In addition, the choices that must be made to implement parareal (division of the temporal domain, election of the coarse solver and so on) are currently made using trial-and-error approaches. Here, we identify the mechanisms responsible for the convergence of parareal of these simulations of drift wave turbulence. We also investigate which conditions these mechanisms impose on any successful parareal implementation. The results reported here should be useful to guide future implementations of parareal within the much wider context of fully-developed fluid and plasma turbulent simulations.     

Statistical-mechanical predictions and Navier-Stokes dynamics of two-dimensional flows on a bounded domain

In this paper the applicability of a statistical-mechanical theory to freely decaying two-dimensional (2D) turbulence on a bounded domain is investigated. We consider an ensemble of direct numerical simulations in a square box with stress-free boundaries, with a Reynolds number that is of the same order as in experiments on 2D decaying Navier-Stokes turbulence. The results of these simulations are compared with the corresponding statistical equilibria, calculated from different stages of the evolution. It is shown that the statistical equilibria calculated from early times of the Navier-Stokes evolution do not correspond to the dynamical quasistationary states. At best, the global topological structure is correctly predicted from a relatively late time in the Navier-Stokes evolution, when the quasistationary state has almost been reached. This failure of the (basically inviscid) statistical-mechanical theory is related to viscous dissipation and net leakage of vorticity in the Navier-Stokes dynamics at moderate values of the Reynolds number.     

Analysis and compression of six-dimensional gyrokinetic datasets using higher order singular value decomposition

Higher order singular value decomposition (HOSVD) is explored as a tool for analyzing and compressing gyrokinetic data. An efficient numerical implementation of an HOSVD algorithm is described. HOSVD is used to analyze the full six-dimensional (three spatial, two velocity space, and time dimensions) gyrocenter distribution function from gyrokinetic simulations of ion temperature gradient, electron temperature gradient, and trapped electron mode driven turbulence. The HOSVD eigenvalues for the velocity space coordinates decay very rapidly, indicating that only a few structures in velocity space can capture the most important dynamics. In almost all of the cases studied, HOSVD extracts parallel velocity space structures which are very similar to orthogonal polynomials. HOSVD is also used to compress gyrokinetic datasets, an application in which it is shown to significantly outperform the more commonly used singular value decomposition. It is shown that the effectiveness of the HOSVD compression improves as the dimensionality of the dataset increases.     

Event-based parareal: A data-flow based implementation of parareal

Parareal is an iterative algorithm that, in effect, achieves temporal decomposition for a time-dependent system of differential or partial differential equations. A solution is obtained in a shorter wall-clock time, but at the expense of increased compute cycles. The algorithm combines a fine solver that solves the system to acceptable accuracy with an approximate coarse solver. The critical task for the successful implementation of parareal on any system is the development of a coarse solver that leads to convergence in a small number of iterations compared to the number of time slices in the full time interval, and is, at the same time, much faster than the fine solver. Very fast coarse solvers may not lead to sufficiently rapid convergence, and slow coarse solvers may not lead to significant gains even if the number of iterations to convergence is satisfactory. We find that the difficulty of meeting these conflicting demands can be substantially eased by using a data-driven, event-based implementation of parareal. As a result, tasks for one iteration do not wait for the previous iteration to complete, but are started when the needed data are available. For given convergence properties, the event-based approach relaxes the speed requirements on the coarse solver by a factor of ～K, where K is the number of iterations required for a converged solution. This may, for many problems, lead to an efficient parareal implementation that would otherwise not be possible or would require substantial coarse solver development. In addition, the framework used for this implementation executes a task when the data dependencies are satisfied and computational resources are available. This leads to improved computational efficiency over previous approaches that pipeline or schedule groups of tasks to a particular processor or group of processors.     

On contour crossings in contour-advective simulations – part 1 – algorithm for detection and quantification

This is the first of two papers devoted to the analysis of contour crossing errors that occur in contour-advective simulations of fluid motion. Here an algorithm is presented for quantifying the error due to contour crossings. The first step is to determine the relative proximity of all possible pairs of contours. A digital representation of each contour is produced to aid in the corresponding calculation. Simple analysis of functions is then used to find any crossings between contours deemed close to each other by the digital representation method. Next, the area in error of a pair of crossing contours is calculated by identifying the polygon or polygons that approximately bound the erroneous region. Finally, some preliminary results of analysis of contour crossings that occur in contour-advective semi-lagrangian (CASL) simulations of single layer quasigeostrophic turbulence are presented. It is shown that the error due to contour crossings is small in the simulations considered here.     

Coupling of turbulence on the ignition of multicomponent sprays

This study examines the effect of turbulence on the ignition of multicomponent surrogate fuels and its role in modifying preferential evaporation in multiphase turbulent spray environments. To this end, two zero-dimensional droplet models are considered that are representative of asymptotic conditions of diffusion limit and the distillation limit are considered. The coupling between diffusion, evaporation and combustion is first identified using a scale analysis of 0D homogeneous batch reactor simulations. Subsequently, direct numerical simulations of homogeneously dispersed multicomponent droplets are performed for both droplet models, in decaying isotropic turbulence and at quiescent conditions to examine competing time scale effects arising from evaporation, ignition and turbulence. Results related to intra-droplet transport and effects of turbulence on autoignition and overall combustion are studied using an aviation fuel surrogate. Depending on the characteristic scale, it is shown that turbulence can couple through modulation of evaporation time or defer the ignition phase as a result of droplet cooling or gas-phase homogenization. Both preferential evaporation and turbulence are found to modify the ignition delay time, up to a factor of two. More importantly, identical droplet ignition behavior in homogeneous gas phase can imply fundamentally different combustion modes in heterogeneous environments.     

涡轮叶栅气热耦合数值方法与验证

应用三阶精度TVD格式和自由型曲面阿格技术,对涡轮内冷叶片进行气热耦合数值模拟.结合商用软件采用多种湍流模型计算方法的结果进行实验验证和对比分析,结果表明,商用软件采用传统湍流模型对温度边界层的模拟是不合理的,采用考虑转捩的湍流模型,调整转捩起始雷诺数,可以较好地模拟温度边界层的热传导.本文对非转捩区边界层温度的计算结果与实验结果吻合较好.     

Simulation of the inherent turbulence and wake interaction inside an infinitely long row of wind turbines

The turbulence in the interior of a wind farm is simulated using large eddy simulation and the actuator line technique implemented in the Navier–Stokes equations. The simulations are carried out for an infinitely long row of turbines simulated by applying cyclic boundary conditions at the inlet and outlet. The simulations investigate the turbulence inherent to the wind turbines as no ambient turbulence or shear is added to this idealised case. The simulated data give insight into the performance of the wind turbines operating in the wake of others as well as details on key turbulent quantities. One of the key features of wakes behind wind turbines is the dynamic wake meandering, which is shown to be related to the wind turbine spacing and the vortex shedding from the turbine as a bluff body. The flow is analysed and reconstructed by applying proper orthogonal decomposition.     

Numerical comparison of Riemann solvers for astrophysical hydrodynamics

The idea of this work is to compare a new positive and entropy stable approximate Riemann solver by Francois Bouchut with a state-of the-art algorithm for astrophysical fluid dynamics. We implemented the new Riemann solver into an astrophysical PPM-code, the Prometheus code, and also made a version with a different, more theoretically grounded higher order algorithm than PPM. We present shock tube tests, two-dimensional instability tests and forced turbulence simulations in three dimensions. We find subtle differences between the codes in the shock tube tests, and in the statistics of the turbulence simulations. The new Riemann solver increases the computational speed without significant loss of accuracy.     

基于高阶累计量的大气光通信自适应信号处理

针对强湍流信道下信号衰落的特点,分析了对数正态分布模型与K分布模型的适用范围.基于K分布模型建立大气光通信接收信号模型,并给出了自适应最优门限检测方法.采用四阶和六阶累计量对强湍流信道参量进行估计,采用二阶累计量对其它高斯噪音进行估计,得到K分布参量及高斯噪音统计量的预测值,实现自适应门限更新.基于Monte Calro算法进行仿真,给出了门限更新算法对通信系统误码率的影响,同时分析了信号采样率对估计参量偏差的影响.计算表明,在强湍流情况下,大气光通信系统的误码率性能得到极大的改善,优于基于MLSD检测的接收机.     

Shell Models of MHD Turbulence and the Problem of Superequipartition

Within the framework of the shell model of turbulence, we consider the long-time evolution of the magnetic field in a turbulent flow of conducting fluid. A weak initial magnetic field rapidly increases up to magnitudes corresponding to the equipartition with kinetic energy, and then the stage of slow evolution begins. It is shown that in some cases, the magnetic energy can significantly exceed the kinetic energy of the turbulence at this stage. We discuss the possible observational evidences for such a superequipartition of the magnetic field. It is shown that the superequipartition is realized if the initial energy of the magnetic field exceeds the kinetic energy, although even in such cases the equipartition is reached in many realizations.     

湍流模型在内流流场数值模拟中的应用

本文将Spalart-Allmaras湍流模型方程推导为守恒形式,并应用于内流湍流流场计算.采用此-方程湍流模型分别对扩压器流场以及NASA 67转子流场进行了数值模拟.结果表明常用在外流计算中的Spalart-Allmaras湍流模型在内流计算中仍具有较高的精度、数值稳定性和效率.     

Turbulence structures in high-speed air flow along a thin cylinder

Turbulent flow in the axial direction along a cylinder representing a monofilament yarn was reproduced for a relatively wide range of radius Reynolds numbers using direct numerical simulations. In the simulation of the thinnest cylinder, the friction coefficient agreed with a previously published formula. A pair of high- and low-speed streaks was detected around even the thinnest cylinder, whereby it was confirmed that turbulence was sustained according to the analysed turbulence statistics. Even when only a single pair of streaks around the cylinder was detected, the characteristics of the turbulence structures, such as the mean streak spacing based on the viscous length scale, were the same as those in flows over a flat plate. It was found that the friction coefficient changes in a way that maintains the structural characteristics of the flow, consistent with the view that universal characteristics of turbulence structures exist.     

卵形钢弹对铝合金靶板侵彻问题的数值模拟

 基于球形空穴膨胀理论（SCE）,采用ABAQUS有限元商业软件并结合其子程序的二次开发功能对钢弹侵彻金属靶进行3D有限元数值模拟。根据空穴膨胀理论,靶体对侵彻弹体的影响可以用一个作用在弹体表面的力函数代替,这样在进行数值模拟时就无须划分靶体网格,也避免了复杂的接触问题,从而使模拟大大简化。模拟所用卵形弹为VAR 4340钢弹,靶体为6061-T6511铝合金。模拟过程中考虑到弹体的可变形性和入射时的微小偏航角等实际情况,并且考虑到了弹身在运动过程中和靶体的接触分离效应。所得模拟结果与文献中的实验结果进行了比较,发现模拟结果与实验结果吻合得很好,并得到了一些有意义的推论。     

新型可压缩尺度在跨声速流动中的应用

基于von Karman长度尺度和新型Reynolds应力本构关系对k-ε湍流模型重构,将k方程封闭,采用代数形式对湍流耗散项进行模化.在KDO（kinetic dependent only）模型的基础上,引入可压缩von Karman长度尺度,得到一种适用于复杂可压缩流动的新型湍流模型CKDO（compressible kinetic dependent only）,在CKDO模型中没有任何经验系数,仅有两个来自边界层精细化标定的可调参数.对RAE2822翼型、轴对称圆筒管道凸起流动、ONERA-M6机翼跨声速流动等算例进行数值计算,结果显示CKDO湍流模型对上述算例流场的压力系数模拟结果与实验值吻合较好,表明CKDO模型能够对跨声速流场进行较为准确的模拟.      

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.     

Entropic, LES and boundary conditions in lattice Boltzmann simulations of turbulence

Large scale (1600³-grid) entropic lattice Boltzmann (ELB) simulations are performed on the 27-bit model at sufficiently high Reynolds numbers to find intermittency corrections to the Kolmogorov k ^-5/3 inertial spectrum. Even though the transport coefficients in ELB and in the Large Eddy Simulation (LES) lattice Boltzmann schemes have very different origins, there are strong similarities in their turbulence statistics from 512³-grid simulations. A new LB moment-space boundary condition algorithm is tested on the 2D backstep problem, with excellent agreement with experimental data even up to a Reynolds number of 800.     

可变形弹丸贯穿铝合金靶的数值模拟

 采用显式动态有限元商业软件ABAQUS/Explicit对可变形卵形弹丸正贯穿和斜贯穿有限厚度铝合金靶的过程进行了有限元数值模拟。根据空穴膨胀理论,将靶体对侵彻的影响用一个作用在弹体表面的力函数代替,同时考虑了有限厚度靶自由表面的影响,并对空穴膨胀得到的力函数进行了修正。这样在进行数值模拟时就无需对靶体划分网格,也避免了复杂的接触问题,从而使模拟大为简化。最后,用VAR4340钢弹贯穿6061-T651铝合金靶板得到的数值模拟结果与实验结果进行了比较,二者基本吻合。     

大气湍流对部分相干厄米-高斯光束空间相干性的影响

基于广义惠更斯-菲涅耳原理,并采用Rytov相位结构函数二次近似,推导出了部分相干厄米-高斯(H-G)光束通过大气湍流传输的光谱相干度公式,研究了湍流对光束的空间相干特性的影响.研究表明,部分相干H-G光束通过大气湍流传输其光谱相干度会出现振荡和相位奇异现象,但随着湍流的增强,振荡减弱,直至振荡和相位奇异现象消失,这一特性与高斯-谢尔模型光束的差异很大.光束的相干参数越小,光束空间相干性受湍流的影响也越小.此外,还研究了光谱相干度二阶矩宽度与光谱强度二阶矩宽度间的关系,得到一些有意义的结果,并给出了合理的 关键词： 部分相干厄米-高斯光束 大气湍流 光谱相干度 二阶矩宽度     

On the role of pressure in elasto-inertial turbulence

The dynamics of elasto-inertial turbulence is investigated numerically from the perspective of the coupling between polymer dynamics and flow structures. In particular, direct numerical simulations of channel flow with Reynolds numbers ranging from 1000 to 6000 are used to study the formation and dynamics of elastic instabilities and their effects on the flow. Based on the splitting of the pressure into inertial and polymeric contributions, it is shown that the polymeric pressure is a non-negligible component of the total pressure fluctuations, although the rapid inertial part dominates. Unlike Newtonian flows, the slow inertial part is almost negligible in elasto-inertial turbulence. Statistics on the different terms of the Reynolds stress transport equation also illustrate the energy transfers between polymers and turbulence and the redistributive role of pressure. Finally, the trains of cylindrical structures around sheets of high polymer extension that are characteristics of elasto-inertial turbulence are shown to be correlated with the polymeric pressure fluctuations.