A control volume finite element method for three-dimensional three-phase flows

A novel control volume finite element method with adaptive anisotropic unstructured meshes is presented for three-dimensional three-phase flows with interfacial tension. The numerical framework consists of a mixed control volume and finite element formulation with a new P₁DG-P₂ elements (linear discontinuous velocity between elements and quadratic continuous pressure between elements). A “volume of fluid” type method is used for the interface capturing, which is based on compressive control volume advection and second-order finite element methods. A force-balanced continuum surface force model is employed for the interfacial tension on unstructured meshes. The interfacial tension coefficient decomposition method is also used to deal with interfacial tension pairings between different phases. Numerical examples of benchmark tests and the dynamics of three-dimensional three-phase rising bubble, and droplet impact are presented. The results are compared with the analytical solutions and previously published experimental data, demonstrating the capability of the present method.     

环境规制强度影响能源效率的门槛效应研究——基于PSTR模型

利用非径向-SBM和CCR模型测算了我国30个省市(暂不包括西藏和港澳台地区)2007-2016年间的环境规制强度以及能源效率,构建面板平滑转移回归模型(PSTR),分析了环境规制强度对我国能源效率的连续非线性变化的影响.研究结果显示,全国环境规制强度对我国能源效率存在非线性效应,二者之间呈倒“U”型关系.环境规制强度小于门槛值0.6376时,环境规制对能源效率产生创新补偿效应,当环境规制强度高于门槛值0.6376时,环境规制对能源效率产生遵循成本效应.而我国东西部地区的环境规制强度与地区能源效率间却存在着与之相反的“U”型效应.     

基于MRS-SJC-Copula模型对A股与港股的动态联动性研究

由于经济增长周期变化,导致不同股票市场存在高低状态转换的现象,在研究不同股票市场之间联动性的研究时,需要考虑股票波动均值和方差两种结构变化。基于具有马尔可夫状态转换的动态SJC-Copula,结合修正ICSS算法对我国内地股票市场和香港股票市场之间的联动性进行方差结构突变点的检验。实证结果表明:国内和香港股票市场之间存在非线性非对称的时变相依性,并持续存在高低两种不同状态的概率转换。股票指数由于动态联动受到负面消息的下跌幅度大于正面消息的变化幅度,且上下尾部均受上期信息的持续影响。“沪港通”、“深港通”、中美贸易战等因素使得其上下尾部发生结构突变,内地与香港股票市场的联动性增大和市场波动幅度趋强。     

Combining Complex and Radial Slave Boson Fields within the Kotliar–Ruckenstein Representation of Correlated Impurities

The gauge symmetry group of any slave boson representation allows to gauge away the phase of bosonic fields. One benefit of this radial field formulation is the elimination of spurious Bose condensations when saddle-point approximation is performed. Within the Kotliar–Ruckenstein representation, three of the four bosonic fields can be radial while the last one has to remain complex. In this work, the procedure to carry out the functional integration involving constrained fermionic fields, complex bosonic fields, and radial bosonic fields is presented. The correctness of the representation is verified by exactly evaluating the partition function and the Green's function of the Hubbard model in the atomic limit.     

Quantum to classical crossover under dephasing effects in a two-dimensional percolation model

Scaling theory predicts complete localization in d = 2 in quantum systems belonging to the orthogonal class(i.e., with timereversal symmetry and spin-rotation symmetry). The conductance g behaves as g^exp(-L/l) with system size L and localization length l in the strong disorder limit. However, classical systems can always have metallic states in which Ohm’s law shows a constant g in d=2. We study a two-dimensional quantum percolation model by controlling dephasing effects. The numerical investigation of g aims at simulating a quantum-to-classical percolation evolution. An unexpected metallic phase, where g increases with L, generates immense interest before the system becomes completely classical. Furthermore, the analysis of the scaling plot of g indicates a metal-insulator crossover.     

Finite element computations of viscoelastic two-phase flows using local projection stabilization

A three-field local projection stabilized (LPS) finite element method is developed for computations of a three-dimensional axisymmetric buoyancy driven liquid drop rising in a liquid column where one of the liquid is viscoelastic. The two-phase flow is described by the time-dependent incompressible Navier-Stokes equations, whereas the viscoelasticity is modeled by the Giesekus constitutive equation in a time-dependent domain. The arbitrary Lagrangian-Eulerian (ALE) formulation with finite elements is used to solve the governing equations in the time-dependent domain. Interface-resolved moving meshes in ALE allows to incorporate the interfacial tension force and jumps in the material parameters accurately. A one-level LPS based on an enriched approximation space and a discontinuous projection space is used to stabilize the numerical scheme. A comprehensive numerical investigation is performed for a Newtonian drop rising in a viscoelastic fluid column and a viscoelastic drop rising in a Newtonian fluid column. The influence of the viscosity ratio, Newtonian solvent ratio, Giesekus mobility factor, and the Eötvös number on the drop dynamics are analyzed. The numerical study shows that beyond a critical Capillary number, a Newtonian drop rising in a viscoelastic fluid column experiences an extended trailing edge with a cusp-like shape and also exhibits a negative wake phenomena. However, a viscoelastic drop rising in a Newtonian fluid column develops an indentation around the rear stagnation point with a dimpled shape.     

A proper orthogonal decomposition variational multiscale meshless interpolating element-free Galerkin method for incompressible magnetohydrodynamics flow

In the recent decade, the meshless methods have been handled for solving most of PDEs due to easiness of the meshless methods. One of the popular meshless methods is the element-free Galerkin (EFG) method that was first proposed for solving some problems in the solid mechanics. The test and trial functions of the EFG are based on the special basis. Recently, some modifications have been developed to improve the EFG method. One of these improvements is the variational multiscale EFG procedure. In the current article, the shape functions of interpolation moving least squares approximation have been applied to the variational multiscale EFG technique for solving the incompressible magnetohydrodynamics flow. In order to reduce the elapsed CPU time of simulation, we employ a reduced-order model based on the proper orthogonal decomposition technique. The current combination can be referred to as the reduced-order variational multiscale EFG technique. To illustrate the reduction in CPU time used as well as the efficiency of the proposed method, we applied it for the two-dimensional cases.     

Uncertainty quantification for dynamics of geometrically nonlinear structures coupled with internal acoustic fluids in presence of sloshing and capillarity

In this paper, we propose an uncertainty quantification analysis, which is the continuation of a recent work performed in a deterministic framework. The fluid–structure system under consideration is the one experimentally studied in the sixties by Abramson, Kana, and Lindholm from the Southwest Research Institute under NASA contract. This coupled system is constituted of a linear acoustic liquid contained in an elastic tank that undergoes finite dynamical displacements, inducing geometrical nonlinear effects in the structure. The liquid has a free surface on which sloshing and capillarity effects are taken into account. The problem is expressed in terms of the acoustic pressure field in the fluid, of the displacement field of the elastic structure, and of the normal elevation field of the free surface. The nonlinear reduced-order model constructed in the recent work evoked above is reused for implementing the nonparametric probabilistic approach of uncertainties. The objective of this paper is to present a sensitivity analysis of this coupled fluid–structure system with respect to uncertainties and to use a classical statistical inverse problem for carrying out the experimental identification of the hyperparameter of the stochastic model. The analysis show a significant sensitivity of the displacement of the structure, of the acoustic pressure in the liquid, and of the free-surface elevation to uncertainties in both linear and geometrically nonlinear simulations.     

基于无人机多光谱图像的土壤水分检测方法研究

以表层土壤为对象,探究土壤的多光谱反射率与土壤水分含量相关性,进行基于无人机多光谱图像的土壤水分含量预测模型方法的探究。选取中国农业大学通州实验站为研究区域,实地采集试验田的土壤样本100组,按照一定梯度配制土壤含水量,配成的土壤含水率为10%~50%之间,土壤含量的真实值采用土壤烘干法进行测定。多光谱相机灵巧便捷,可搭载在无人机上对土壤进行监测。将RedEdged-M型多光谱相机搭载在Phantom 3型无人机上,选择阳光充足的采集环境,实时采集土壤样本的多光谱图像,建立土壤多光谱信息与水分含量之间的模型。利用处理光谱数据的ENVI5.3软件提取土壤样本多光谱信息,以多光谱相机自带的标准白板反射率为100%,计算出土壤样本在蓝、绿、红、红边、近红外五个波段的光谱反射率。采用BP神经网络算法、支持向量机算法、偏最小二乘算法分别建立基于无人机多光谱图像的土壤水分含量的预测模型。以80组土壤样本数据作为训练集,建立基于多光谱图像的土壤水分含量预测模型。采用莱文贝格-马夸特算法对BPNN进行改进,提高了其训练速度,当网络结构为5-10-1时,训练效果最好,本文选择该网络结构;SVM采取高斯核函数,当参数为0.56时,模型效果最好。本研究采用归一化均方根误差(NRMSE)和决策系数(R 2)对三种土壤水分含量的预测模型进行定量对比。以20组土壤样本数据作为测试集,结果可知,基于BP神经网络土壤水分含量预测模型的NRMSE为0.268,R 2为0.872;基于支持向量机的土壤水分含量预测模型的NRMSE为0.298,R 2为0.821;基于偏最小二乘土壤水分含量预测模型的NRMSE为0.316,R 2为0.789。对三种模型分析可知,基于BPNN的土壤水分含量预测模型效果均较好。结果可知,土壤的光谱反射率与含水率间存在较密切的相关性,将多光谱相机搭载在无人机上可以对土壤水分含量进行有效的实时监测,对监测土壤墒情提供技术支持和理论支撑。