A hybrid subcell-remapping algorithm for staggered multi-material arbitrary Lagrangian-Eulerian methods

A new flux-based hybrid subcell-remapping algorithm for staggered multimaterial arbitrary Lagrangian-Eulerian (MMALE) methods is presented. This new method is an effective generalization of the original subcell-remapping method to the multi-material regime (LOUBERE, R. and SHASHKOV,M. A subcell remapping method on staggered polygonal grids for arbitrary-Lagrangian-Eulerian methods. Journal of Computational Physics, 209, 105–138 (2005)). A complete remapping procedure of all fluid quantities is described detailedly in this paper. In the pure material regions, remapping of mass and internal energy is performed by using the original subcell-remapping method. In the regions near the material interfaces, remapping of mass and internal energy is performed with the intersection-based fluxes where intersections are performed between the swept regions and pure material polygons in the Lagrangian mesh, and an approximate approach is then introduced for constructing the subcell mass fluxes. In remapping of the subcell momentum, the mass fluxes are used to construct the momentum fluxes by multiplying a reconstructed velocity in the swept region. The nodal velocity is then conservatively recovered. Some numerical examples simulated in the full MMALE regime and several purely cyclic remapping examples are presented to prove the properties of the remapping method.

An efficient algorithm to compute transient pressure responses of slanted wells with arbitrary inclination in reservoirs

Compared with vertical and horizontal wells, the solution and computation of transient pressure responses of slanted wells are more complex. Vertical and horizontal wells are both simplified cases of slanted wells at particular inclination, so the model for slanted wells is more general and more complex than other models for vertical and horizontal wells. Many authors have studied unsteady-state flow of fluids in slanted wells and various solutions have been proposed. However, until now, few of the published results pertain to the computational efficiency. Whether in the time domain or in the Laplace domain, the computation of integration of complex functions is necessary in obtaining pressure responses of slanted wells, while the computation of the integration is complex and time-consuming. To obtain a perfect type curve the computation time is unacceptable even with an aid of high-speed computers. The purpose of this paper is to present an efficient algorithm to compute transient pressure distributions caused by slanted wells in reservoirs. Based on rigorous derivation, the transient pressure solution for slanted wells of any inclination angle is presented. Assuming an infinite-conductivity wellbore, the location of the equivalent-pressure point is determined. More importantly, according to the characteristics of the integrand in a transient pressure solution for slanted wells, the whole integral interval is partitioned into several small integral intervals, and then the method of variable substitution and the variable step-size piecewise numerical integration are employed. The amount of computation is significantly reduced and the computational efficiency is greatly improved. The algorithm proposed in this paper thoroughly solved the difficulty in the efficient and high-speed computation of transient pressure distribution of slanted wells with any inclination angle.

Single-Step Arbitrary Lagrangian-Eulerian Discontinuous Galerkin Method for 1-D Euler Equations

We propose an explicit,single-step discontinuous Galerkin method on moving grids using the arbitrary Lagrangian-Eulerian approach for one-dimensional Euler equations.The grid is moved with the local fluid velocity modified by some smoothing,which is found to con-siderably reduce the numerical dissipation introduced by Riemann solvers.The scheme preserves constant states for any mesh motion and we also study its positivity preservation property.Local grid refinement and coarsening are performed to maintain the mesh qual-ity and avoid the appearance of very small or large cells.Second,higher order methods are developed and several test cases are provided to demonstrate the accuracy of the proposed scheme.

Negative Norm Estimates for Arbitrary Lagrangian-Eulerian Discontinuous Galerkin Method for Nonlinear Hyperbolic Equations

In this paper,we present the negative norm estimates for the arbitrary Lagrangian-Eulerian discontinuous Galerkin(ALE-DG)method solving nonlinear hyperbolic equations with smooth solutions.The smoothness-increasing accuracy-conserving(SIAC)filter is a post-processing technique to enhance the accuracy of the discontinuous Galerkin(DG)solutions.This work is the essential step to extend the SIAC filter to the moving mesh for nonlinear problems.By the post-processing theory,the negative norm estimates are vital to get the superconvergence error estimates of the solutions after post-processing in the L2 norm.Although the SIAC filter has been extended to nonuniform mesh,the analysis of fil-tered solutions on the nonuniform mesh is complicated.We prove superconvergence error estimates in the negative norm for the ALE-DG method on moving meshes.The main dif-ficulties of the analysis are the terms in the ALE-DG scheme brought by the grid velocity field,and the time-dependent function space.The mapping from time-dependent cells to reference cells is very crucial in the proof.The numerical results also confirm the theoreti-cal proof.

A Novel Memory Compress Algorithm for Arbitrary Waveform Generator

A memory compress algorithm for 12\|bit Arbitrary Waveform Generator (AWG) is presented and optimized. It can compress waveform memory for a sinusoid to 16×13bits with a Spurious Free Dynamic Range (SFDR) 90.7dBc (1/1890 of uncompressed memory at the same SFDR) and to 8×12bits with a SFDR 79dBc. Its hardware cost is six adders and two multipliers. Exploiting this memory compress technique makes it possible to build a high performance AWG on a chip.

不同截面肋柱-软尾结构单相流动传热比较

基于任意拉格朗日-欧拉(ALE)方法,利用动网格技术和重叠网格技术数值模拟研究了不同Reynolds数、截面形状以及长径比下的肋柱-软尾结构在通道中的双向流固耦合换热问题。模拟工况为:Reynolds数Re=200,275,351;肋柱截面形状:圆形和方形;长径比k=2,3,4。研究表明:Re=275时圆形截面肋柱-软尾结构的流动换热综合能力优于方形截面结构,k=3时圆形截面肋柱-软尾结构的流动换热综合能力最佳,肋柱周围的局部换热能力方形截面结构好于圆形截面结构;k=3时,随着Reynolds数的增大,不同截面形状的肋柱-软尾结构的流动换热综合能力逐渐升高,并且高Reynolds数、高长径比的圆形截面综合流动换热能力最佳;与不加软尾肋柱结构的流动换热能力进行对比发现,对于圆形截面形状的肋柱结构,增加软尾后综合换热能力增大了19.46%。

Arbitrary Lagrangian‑Eulerian Discontinuous Galerkin Methods for KdV Type Equations

In this paper,several arbitrary Lagrangian-Eulerian discontinuous Galerkin(ALE-DG)methods are presented for Korteweg-de Vries(KdV)type equations on moving meshes.Based on the L^(2) conservation law of KdV equations,we adopt the conservative and dissipative numerical fuxes for the nonlinear convection and linear dispersive terms,respectively.Thus,one conservative and three dissipative ALE-DG schemes are proposed for the equations.The invariant preserving property for the conservative scheme and the corresponding dissipative properties for the other three dissipative schemes are all presented and proved in this paper.In addition,the L^(2)-norm error estimates are also proved for two schemes,whose numerical fuxes for the linear dispersive term are both dissipative type.More precisely,when choosing the approximation space with the piecewise kth degree polynomials,the error estimate provides the kth order of convergence rate in L^(2)-norm for the scheme with the conservative numerical fuxes applied for the nonlinear convection term.Furthermore,the(k+1∕2)th order of accuracy can be proved for the ALE-DG scheme with dissipative numerical fuxes applied for the convection term.Moreover,a Hamiltonian conservative ALE-DG scheme is also presented based on the conservation of the Hamiltonian for KdV equations.Numerical examples are shown to demonstrate the accuracy and capability of the moving mesh ALE-DG methods and compare with stationary DG methods.

基于ALE算法的高速水射流对船体表面冲击特性研究

为探究水射流清洗附着物对船体表面的损伤影响,基于ALE算法研究了不同入射角θ和不同流速v冲击船体表面过程中射流的冲击压力特征和应力特征。结果显示,随着入射角θ增大,靶件所受冲击压力会出现水锤压力与滞止压力阶段。高压水射流动能在适当入射角θ增加,入射角过大(θ=20°)反而会使其降低。以一定入射角θ冲击靶体时,由于剪切效应加强靶体表面与内部应力分布比垂直冲击时更复杂,得出对船体表面材料影响最小的参数组合和最大主应力与射流参数入射角和速度的拟合公式。研究结果对水射流清洗船体表面附着物的应用具有较好的理论意义与实际应用价值。

鱼雷垂直入水瞬间结构响应的数值模拟

垂直入水的鱼雷在短时间内弹道稳定,基于此,针对跨介质鱼雷撞水冲击造成的结构问题展开研究,探究了各舱段壳体和连接部位的轴向运动规律及受力特性,利用任意拉格朗日-欧拉算法及罚函数法建立了流固耦合数值模型,并对其合理性和网格无关性进行了验证。对采用不同连接方式的4种头型鱼雷分别模拟,并与整体式鱼雷进行了对比。结果表明:鱼雷撞水后加速度瞬间升高,头型越尖,所受的冲击越小;由于应力以波的形式向后传递,因此各舱段会依照距离头部的远近依次响应,且强度逐渐减弱;相邻壳体的相对静止状态被打破,运动过程中会不断拉压连接件,使之形状和位置都发生较大变化;壳体相互远离时,雷体外缘产生缝隙,此时连接件应力也达到最大,对连接的稳固性不利。因此,建议工程中增加密封圈或其他固定装置等,以加强对连接部位的保护。

应用构型一致的显式方法预测结构冲击动响应

目的 发展构型一致的显式方法,以提高拉格朗日有限元对冲击、碰撞及侵彻问题计算的精度和健壮性。方法 为更准确地描述和计算结构大变形,基于任意参考构型理论,建立构型一致的动量方程拉格朗日有限元格式。为避免网格间侵入现象,通过结合前增量位移的时间积分方法和共轭梯度算法,使得显式增量步更新后,仍满足接触非侵入条件。结果 通过对大变形碰撞及侵彻问题的模拟,并与LS-DYNA软件结果对比,验证了计算方法的可靠性。结论 基于构型一致的显式算法可有效抑制大变形碰撞过程的单元畸变,提高计算程序的健壮性和预测准确度,使该算法在模拟大变形碰撞问题方面具有优势。

爆裂轮胎精确建模及其动态特性仿真方法研究

汽车行驶中轮胎突然爆裂是极其危险的行驶工况,但轮胎爆裂过程的准确测试分析难度很大,而其现有仿真方法因需大幅简化使得难以描述轮胎爆裂过程的瞬态特性。针对此问题,本文中提出分别模拟胎内、外空气,且考虑轮胎各种材料失效特性、胎内空气与轮胎车轮总成流-固耦合的汽车轮胎爆裂过程仿真分析方法,实现轮胎滚动中爆胎过程的瞬态动力学特性仿真;并通过对比仿真和理论计算结果,验证仿真模型的正确性;同时,通过计算还获得爆裂轮胎内部空气泄漏规律和路面对轮胎径向力的变化特性,以及轮胎速度、胎压与裂口尺寸对爆胎过程持续时间和轮胎力学特性的影响机理。本文工作聚焦于仿真方法研究,对掌握爆裂轮胎瞬态特性、研究爆胎后整车动力学控制策略具有意义。

Second-Order Invariant Domain Preserving ALE Approximation of Euler Equations

An invariant domain preserving arbitrary Lagrangian-Eulerian method for solving non-linear hyperbolic systems is developed.The numerical scheme is explicit in time and the approximation in space is done with continuous finite elements.The method is made invar-iant domain preserving for the Euler equations using convex limiting and is tested on vari-ous benchmarks.

ALE框架下几种不同Godunov型格式的数值比较

给出一种有限体积Godunov型的ALE方法,用于求解多介质大变形的可压缩流动问题.由于方法具有任意的网格移动速度,可在拉氏、欧氏和ALE之间切换,具有较强的适应性.通过数值算例对这3种框架下的数值特性进行了比较研究.同时还研究了几种不同Godunov型格式的数值行为特性,分析比较了它们对激波和接触间断的分辨效果.

基于DEM的任意方向坡度计算方法

坡度是数字地形分析中重要的地形因子,在水文分析、土壤侵蚀模拟、地貌类型划分等地学分析及工程上均有广泛的应用。由于地形的各向异性,坡度在各个方向上并不相同。目前,基于DEM所提取的坡度,均是位于最陡方向上的坡度,而任意给定方向坡度计算是地学分析和工程应用中较为常见的问题。在对目前DEM坡度提取算法研究的基础上,通过数学分析,给出了格网DEM上任意方向格网点的坡度计算模型和计算流程,并给出了相应的计算实例,从而将坡度计算模型从特定方向推向任意方向,使DEM坡度计算更具普适性。

任意形状工作面沉陷预测的概率积分法及其应用

概率积分法是煤矿开采沉陷预测的重要方法,可适用于缓倾斜、倾斜煤层开采地表移动分布曲线符合正态分布规律的地表移动和变形计算。针对原方法对任意形状工作面存在的不足,在原有走向和倾向概率积分函数的基础上,以走向和倾向为基准划分积分函数区域,在该区域内剖分非结构化的三角形单元作为二重积分的基本单位;通过坐标旋转变换的二重积分换元法,转化为以直线为上、下限的二重积分,计算旋转后的影响半径,对新的二重积分采用复合辛普森数值积分公式,积分得出地表任意点在基本三角形开采单元下的积分下沉值;最后,通过叠加计算完成任意点、任意形状工作面概率积分法的沉陷预测计算。算法在GIS系统下实现,实例应用效果良好,可为"三下"采煤提供地表移动预测计算的支持。

Chameleon算法的改进

结合Chameleon算法可以发现高质量的任意形状、大小和密度的自然簇及一趟聚类算法快速高效的特点,研究可以处理混合属性的高效聚类算法.首先简单改进Chameleon算法,使之可以处理含分类属性的数据;进而提出一种两阶段聚类算法.第一阶段使用一趟聚类算法对数据集进行初始划分,第二阶段利用改进的Chameleon算法归并初始划分而得到最终聚类.在真实数据集和人造数据集上的实验结果表明,提出的两阶段聚类算法是有效可行的.

一种新型遗传算法及其在土坡任意滑动面确定中的应用

提出了一种便于工程应用的改进模拟任意滑动面策略。针对简单遗传算法容易陷入局部最优值的缺陷,借鉴和声算法产生新解的方式来产生遗传算法中的子代个体。该策略能综合利用整个父体的信息来构建子代。将该方法用于求解两个复杂土坡的最小安全系数,所得结果与已有文献结果比较证明,新型遗传算法能搜索到更小的安全系数,可应用于土坡稳定分析。

塔里木地区勘探地震正演模拟研究

以塔里木前陆盆地地质背景为模型,采用三维任意差分精细积分方法并行算法实现了库车地区三维正演模拟.三维任意差分精细积分方法通过时间域采用局部积分半解析方法求得波动方程的递推算子,与常规的差分法相比计算精度有较大提高;文中计算稳定性根据实际算例进行分析,采用稳定因子约束,得到较好的稳定性;边界条件采用改进的自适应吸收边界,并通过串行程序并行化,大大减少了三维正演模拟的耗时,完成了大数据量三维正演模拟.

基于遗传算法的边坡稳定性分析

边坡稳定性分析的关键是如何确定最危险滑动面。遗传算法是一种全局优化分析方法,克服了一般优化方法容易陷入局部最优解的缺点。由于工程实际中边坡几何形状的不规则和材料的非均匀性,真正的临界滑动面形状并不是都能用圆弧来准确描述的,研究任意型滑面情况下的稳定性很有必要。为更加合理地进行边坡的稳定性分析,利用遗传算法来搜索模拟边坡的最危险滑动面,在工程实例中进行具体应用,得到了非圆弧型滑动面,与其他软件计算结果对比,表明本文算法精度更高,适应性更广。