炸药爆轰物质点法三维数值模拟

炸药爆轰以及多点起爆所产生的爆轰波汇聚问题很难应用有限元法进行模拟分析,尤其当网格发生畸变时,导致有限元法计算效率和数值精度严重下降,甚至无法得到正确结果.为此,该文应用显式积分算法的物质点法对炸药两点起爆和按时间序列的多点起爆的爆轰过程进行数值模拟,与炸药爆轰的理论计算结果相吻合.物质点法不但可以有效地避免网格畸变问题,而且为炸药爆轰的数值模拟提供了新的思路.     

Point interactions for 3D sub-Laplacians

In this paper we show that, for a sub-Laplacian Δ on a 3-dimensional manifold M, no point interaction centered at a point $q_0\in M$ exists. When M is complete w.r.t. the associated sub-Riemannian structure, this means that Δ acting on $C_0^{\infty }(M?\{q_0\})$ is essentially self-adjoint in $L^2(M)$. A particular example is the standard sub-Laplacian on the Heisenberg group. This is in stark contrast with what happens in a Riemannian manifold N, whose associated Laplace-Beltrami operator acting on $C_0^{\infty }(N?\{q_0\})$ is never essentially self-adjoint in $L^2(N)$, if $\dim ?N\le 3$. We then apply this result to the Schrödinger evolution of a thin molecule, i.e., with a vanishing moment of inertia, rotating around its center of mass.     

Point Defect in a Nonlocal Elastic Medium

We investigate the stress field in the vicinity of a point defect in a nonlocal elastic solid. Unlike the classical solution, the stress field has no singularities. We estimate the values of the elastic energy of a defect and maximum stresses.     

Meshfree Thinning of 3D Point Clouds

An efficient data reduction scheme for the simplification of a surface given by a large set X of 3D point-samples is proposed. The data reduction relies on a recursive point removal algorithm, termed thinning, which outputs a data hierarchy of point-samples for multiresolution surface approximation. The thinning algorithm works with a point removal criterion, which measures the significances of the points in their local neighbourhoods, and which removes a least significant point at each step. For any point x in the current point set Y⊂X, its significance reflects the approximation quality of a local surface reconstructed from neighbouring points in Y. The local surface reconstruction is done over an estimated tangent plane at x by using radial basis functions. The approximation quality of the surface reconstruction around x is measured by using its maximal deviation from the given point-samples X in a local neighbourhood of x. The resulting thinning algorithm is meshfree, i.e., its performance is solely based upon the geometry of the input 3D surface point-samples, and so it does not require any further topological information, such as point connectivities. Computational details of the thinning algorithm and the required data structures for efficient implementation are explained and its complexity is discussed. Two examples are presented for illustration. This paper is dedicated to Arieh Iserles on the occasion of his 60th anniversary.     

一种3D仿真机房模型分析

本文讨论一种合理的绿色机房模型,求出了在不同的任务量、分配方式、空调风速和空调温度下机房的平均温度、热点、以及热分布和气流速度分布图。分别用人工神经网络和模拟仿真软件Airpak 软件建立模型分析空调的热分布。通过在Airpak中更改机柜发热功率、空调的送风温度、送风速度来模拟仿真不同情况下机房的热循环过程。最后进行改进和优化,使其能够适应更多情况和条件。     

Simulation of human ischemic stroke in realistic 3D geometry

In silico research in medicine is thought to reduce the need for expensive clinical trials under the condition of reliable mathematical models and accurate and efficient numerical methods. In the present work, we tackle the numerical simulation of reaction–diffusion equations modeling human ischemic stroke. This problem induces peculiar difficulties like potentially large stiffness which stems from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of steep spatial gradients in the reaction fronts, spatially very localized. Furthermore, simulations on realistic 3D geometries are mandatory in order to describe correctly this type of phenomenon. The main goal of this article is to obtain, for the first time, 3D simulations on realistic geometries and to show that the simulation results are consistent with those obtain in experimental studies or observed on MRI images in stroke patients.For this purpose, we introduce a new resolution strategy based mainly on time operator splitting that takes into account complex geometry coupled with a well-conceived parallelization strategy for shared memory architectures. We consider then a high order implicit time integration for the reaction and an explicit one for the diffusion term in order to build a time operator splitting scheme that exploits efficiently the special features of each problem. Thus, we aim at solving complete and realistic models including all time and space scales with conventional computing resources, that is on a reasonably powerful workstation. Consequently and as expected, 2D and also fully 3D numerical simulations of ischemic strokes for a realistic brain geometry, are conducted for the first time and shown to reproduce the dynamics observed on MRI images in stroke patients. Beyond this major step, in order to improve accuracy and computational efficiency of the simulations, we indicate how the present numerical strategy can be coupled with spatial adaptive multiresolution schemes. Preliminary results in the framework of simple geometries allow to assess the proposed strategy for further developments.     

煤层压裂裂缝三维延伸模拟及产量预测研究

针对煤层气井的压裂特点和产出机理,综合应用流体力学、线弹性断裂力学、传热学、计算数学和软件工程等方面的知识,提出了煤层压裂裂缝三维延伸模型和产量动态预测模型,其中裂缝三维延伸模型考虑了煤层、上下遮挡层之间的地应力和岩石力学参数变化的影响,产量动态预测模型考虑了煤层气先解吸扩散后渗流入井的产出机理。在此基础上研制了煤层气井三维压裂优化设计软件,并通过实例计算验证了其实用性和可靠性。     

三维矩形槽道中颗粒沉降的数值模拟

采用三维格子Boltzmann方法对矩形通道中的颗粒沉降进行了模拟研究．单颗粒沉降的模拟结果表明,颗粒最终的稳定沉降位置沿槽道中心线,不受颗粒初始位置和直径的影响．颗粒和壁面之间的两体相互效应可以用无因次沉降速度定量描述,无因次沉降速度的模拟结果和实验结果定量上吻合一致．模拟分析了双颗粒沉降的DKT（drafting, kissing and tumbling）过程,探讨了颗粒直径比以及壁面效应对DKT过程的影响．模拟发现当颗粒直径相同时,双颗粒的沉降过程为周期性的DKT过程,从而形成双螺旋形式的沉降轨迹,此螺旋沉降轨迹的频率和振幅受颗粒初始位置影响．从模拟结果中还得到颗粒群的最终稳定构型,并进行了构型对比分析．最后对包含49个颗粒的颗粒群沉降行为进行了模拟,说明多体相互作用在对称性的情况下可以简化．     

Simulation of the gelation process of hydrogel droplets in 3D bioprinting

The aim of this work is to numerically simulate the gelation of a crosslinking polymer, which is a very complex process involving chemical reactions and phase transitions from a viscous fluid to a viscoelastic solid. A phenomenological model is proposed to simulate the gelation process of agarose droplets, considering the thermal boundary conditions. The numerical model is implemented using the finite element package FlexPDE. The temperature- and time-dependent degree of gelation and the deformation of the droplets during the gelation process are investigated. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

径向基网络的非线性插值与3D点云曲面重构技术

研究了径向基网络插值算法与3D曲面重构方法,分别从研究价值、插值理论、仿真等等方面做了详细分析,研究结果表明RBF-Network在逼近一维复杂的非线性函数时具有收敛速度快、精度高、泛化能力更强等优点.但在3D重构方面,基于RBF的单位分解法重构效果更好.     

Simulation Studies of Some Voronoi Point Processes

We introduce a new class of dynamic point process models with simple and intuitive dynamics that are based on the Voronoi tessellations generated by the processes. Under broad conditions, these processes prove to be ergodic and produce, on stabilisation, a wide range of clustering patterns. In the paper, we present results of simulation studies of three statistical measures (Thiel’s redundancy, van Lieshout and Baddeley’s J-function and the empirical distribution of the Voronoi nearest neighbours’ numbers) for inference on these models from the clustering behaviour in the stationary regime. In particular, we make comparisons with the area-interaction processes of Baddeley and van Lieshout.     

人口迁移模型的改进及系统动力学仿真预测

求出了Keyfitz模型和Rogers模型的理论解,并以Rogers模型为例,对人口迁移模型进行了改进,使之适用范围更广.在人口迁移模型的基础上,建立了系统动力学模型,并对江西省的人口迁移问题进行了仿真预测,模拟出了江西省农村人口、城镇人口及城市化率的变化趋势.     

基于三维CFD-DEM的多孔介质流场数值模拟

将多孔介质局部细观流动与基于Darcy定律的宏观物理模型相结合,应用三维CFD-DEM对多孔介质流场进行局部细观数值模拟,得到多孔介质的惯性阻力系数和粘性阻力系数.并将其作为参数提供给基于Darcy定律的CFD多孔介质模型,从而可用于更大规模的多孔介质流场计算.应用Voronoi多面体作为网格单元,解决了CFD DEM中网格孔隙率精确计算的困难.文中发展的多尺度结合应用的研究方法,在计算精度和计算效率的矛盾中找到了较好的平衡,对于工程应用而言,有节约实验成本、提高计算结果可靠性的功效.     

矿区土壤中含水率及重金属迁移转化的数值模拟

本文基于由连续性方程和达西定律所推出的土壤中水分运动基本方程,以一维垂向水分方程为研究对象,构造稳定收敛的有限差分格式,运用MATLAB数学工具,对地面饱水情况下土壤水分运动的一维垂向方程进行了数值模拟,得到了土壤中水分的迁移规律;同时,综合考虑对流扩散作用以及土壤对重金属的吸附解吸作用,利用非饱和土壤中重金属离子迁移转化模型,对锌离子在矿区土壤中的迁移转化进行了数值模拟,展示了锌离子在矿区土壤中的浓度分布规律．     

Boosted Surfaces: Synthesis of Meshes using Point Pair Generators as Curvature Operators in the 3D Conformal Model

This paper introduces a new technique for the formulation of parametric surfaces. Applying translation operations to tangent vectors ${n_{\circ} {\bf \upsilon}}$ results in null point pairs ${\tau}$ . We treat these null point pairs as surface and mesh curvature control points which can be interpolated and exponentiated to construct continuous topological transformations ${\mathcal{K}}$ of the form ${e^{{-}\frac{\tau}{2}}}$ 2. Some basic algorithms are proposed, including the boost which bends a line to a circle of curvature ${\kappa}$ , and the twisted boost which generates the Hopf fibration. We investigate methods to control curvature in two orthogonal directions u and v and examine a few distance-based and linear weighting techniques for synthesizing surface patches using multiple curvature control points. We consider the expressivity of the technique in manipulating meshes, and find that applying these rotors to mesh points provides a novel and computationally efficient method for creating boosted forms.     

非Newton流体的物质点法模拟研究

准确模拟非Newton流体的运动特性具有重要的工程意义.物质点法作为一种相对新兴的粒子型算法,其结合了Lagrange算法和Euler算法的双重优势,已广泛有效地应用于各个工程领域.基于物质点法,结合人工状态方程,分析了两种非Newton流体(cross流体和幂律流体)在平板Poiseuille流和Couette流情况下的流动特性.结果表明:对Newton流体,物质点模拟结果与理论值一致;对非Newton流体,物质点法可准确模拟其剪切稀化和剪切稠化现象.表明了物质点法在模拟非Newton流体流动问题时的适用性,拓展了物质点法的应用范围.     

Formulation and Numerical Implementation of Ferroelectrics at Large Strains

In recent years, an increasing interest has been shown in functional materials such as ferroelectric polymers. For such materials, viscous effects and electric polarizations cause hysteresis phenomena accompanied with possibly large remanent strains and rotations. Ferroelectric polymers have many attractive characteristics. They are light, inexpensive, fracture tolerant, and pliable. Furthermore, they can be manufactured into almost any conceivable shape and their properties can be tailored to suit a broad range of requirements. In this work, continuous and discrete variational formulations are exploited for the treatment of the non-linear dissipative response of ferroelectric polymers under electrical loading. The point of departure is a general internal variable formulation that determines the hysteretic response of this class of materials in terms of an energy storage and a rate-dependent dissipation function. The ferroelectric constitutive assumptions, which account for specific problems arising in the geometric nonlinear setting, are discussed. With regard to the choice of the internal variables, a critical factor is the kinematic assumptions. Here, we propose the multiplicative decomposition of the local deformation gradient into reversible and remanent parts, where the latter is characterized by a metric tensor. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

3D Euler spirals for 3D curve completion

Shape completion is an intriguing problem in geometry processing with applications in CAD and graphics. This paper defines a new type of 3D curve, which can be utilized for curve completion. It can be considered as the extension to three dimensions of the 2D Euler spiral. We prove several properties of this curve - properties that have been shown to be important for the appeal of curves. We illustrate its utility in two applications. The first is “fixing” curves detected by algorithms for edge detection on surfaces. The second is shape illustration in archaeology, where the user would like to draw curves that are missing due to the incompleteness of the input model.     

A Co-Simulation Approach for the 3D Dynamic Simulation of Vehicles Considering Sloshing in Cargo and Fuel Tanks

The sloshing of liquids in cargo and fuel tanks mounted on vehicles can have a significant influence on the vehicle's driving dynamics and stability. To evaluate and optimize the quality of tank designs, we propose a co-simulation approach that consists of a coupled multibody system simulation for the vehicle and a Discrete Element Method and Smoothed Particle Hydrodynamics simulation for the sloshing cargo. This approach is beneficial especially for the simulation of fluid cargos, as Smoothed Particle Hydrodynamics does not require additional models to track and reconstruct free fluid surfaces. By means of dynamic 3D simulations of a double lane change maneuvers we compare the two different cargo models and demonstrate the viability of the co-simulation approach. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)