A Computational Framework for Parachute Inflation Based on Immersed Boundary/Finite Element Approach

A computational framework for parachute inflation is developed based on the immersed boundary/finite element approach within the open-source IBAMR library.The fluid motion is solved by Peskin's diffuse-interface immersed boundary(IB)method,which is attractive for simulating moving-boundary flows with large deformations.The adaptive mesh refinement technique is employed to reduce the computational cost while retain the desired resolution.The dynamic response of the parachute is solved with the finite element approach.The canopy and cables of the parachute system are modeled with the hyperelastic material.A tether force is introduced to impose rigidity constraints for the parachute system.The accuracy and reliability of the present framework is validated by simulating inflation of a constrained square plate.Application of the present framework on several canonical cases further demonstrates its versatility for simulation of parachute inflation.

Adaptive Finite Element Method for Steady Convection-Diffusion Equation

This paper examines the numerical solution of the convection-diffusion equation in 2-D. The solution of this equation possesses singularities in the form of boundary or interior layers due to non-smooth boundary conditions. To overcome such singularities arising from these critical regions, the adaptive finite element method is employed. This scheme is based on the streamline diffusion method combined with Neumann-type posteriori estimator. The effectiveness of this approach is illustrated by different examples with several numerical experiments.

降阶单元的新进展:内置了最大模误差估计器的自适应有限元法初探

该文基于初值问题中降阶单元的成功实践,进一步对一般边值问题提出无需超收敛计算、无需结构化网格、无需结点位移修正的降阶单元;进而提出以降阶单元作为最终解,且内置了最大模误差估计器的自适应有限元算法。该文对这一研究进展做简要介绍,并给出一维和二维边值问题的初步算例,以展示本法的可行性、有效性和可靠性。

内置了最大模误差估计器的自适应有限元法——研究进展与展望

新近提出的降阶单元,将常规单元解答的最高次项视为误差项,当作内置的最大模误差估计器;将降低一次的解作为有限元最终解,从而一举实现了按最大模控制误差的自适应有限元算法。降阶单元最初针对结构时程分析的自适应步长算法提出,同时将其推广到一般的一维初值问题和边值问题。其后,将其推广到二维边值问题,构造了任意四边形和三角形降阶单元,已成功求解弹性薄膜挠度、弹性力学平面问题、平面和反平面裂纹问题、中厚板弯曲问题等各类二维问题。近期,又进一步将其推广到诸如非线性初值问题、薄膜结构找形问题、最小曲面问题、薄膜与地基接触、弹塑性扭转问题等非线性问题。该文对这一系列研究进展做了综述性介绍和展望,并给出各类问题的代表性数值算例以展示本法的有效性、灵活性、通用性和可靠性。

VLSI三维寄生电容提取的层次式h-自适应计算

在基于直接边界元素法的层次式 h-自适应计算中 ,改进了层次式边界元的自动加密方法 ,提高了计算可靠性 .同时 ,将基于超收敛恢复技术的误差指示器实现于在常数元基础上叠加层次锥函数的寄生电容自适应计算 ,提出一种在不同阶次边界元上使用恢复技术的方法 .与同类软件相比 ,计算稳定 。

基于改进四叉树和比例边界有限元法的自适应设计域拓扑优化方法

针对大型结构拓扑优化计算成本高和固体各向同性材料惩罚模型(SIMP)在优化后结构边界处求解精度低的问题,提出了一种基于SIMP法的自适应设计域(ADD)拓扑优化方法。将改进四叉树法应用在拓扑优化的过程中,通过自动划分不同等级的网格单元来减少网格数量、减轻计算负担并提高边界处求解精度;采用比例边界有限元法(SBFEM)实时计算划分后结构的有限元信息,解决了不同等级网格间悬挂节点的问题。所提方法可在初始网格相对较少的情况下得到更加精确的结果,大幅度地降低了计算成本。数值算例结果表明,所提方法在最终结构边界处精度相同的情况下,计算时间最快可缩短为原来的1/100,可以为后续降低大型结构拓扑优化的计算成本提供参考。

基于模糊逻辑系统的H-R自适应边界元误差估计

为克服在利用传统自适应边界元法求解弹性问题时需对不同问题设计不同误差估计公式的缺点,以专家经验为基础,利用模糊逻辑理论,提出一种新的误差分析方法.基于H-R自适应边界元法,用FORTRAN编写求解2个经典平面弹性静力学问题的程序.分析表明该误差分析方法能较好地估计边界元解的误差.

h-层状自适应边界元方法的算法

给出了 h-层状自适应边界元方法的基本算法 ,并介绍了应用这一算法编写的求解平面弹性静力学问题的计算机程序 Elquahhbe。这个程序中包含一些新的内容 :它的自适应细分过程通过一个新型的误差指示因子加以驱动 ;整个细分过程的信息都压缩到两组“指针”数组中 ,对“指针”数组进行简单运算即可得到生成离散网格和装配系统矩阵所需的信息 ,因此较好地解决了数据管理中存储与导出的矛盾。数值算例证明这些方法是行之有效的。

h-自适应边界元方法的插值残差计算及误差估计

本文提出了一种用于估计h-自适应边界元过程解误差的新方法。这种方法基于h-自适应边界元过程生成的离散网格,通过计算近似解的插值残差,以此作为误差估计的依据。此外,这种误差分析方法方法易于程序化,可以很方便地接入现有h-自适应边界元计算机程序(简单细分或分层细分),而对原程序不作大的改动。通过对二个经典的弹性静力学问题的分析表明:本文的方法能较好地估计边界元解的误差,并使h-自适应边界元程序的分析更加有效可靠。

An adaptive scaled boundary finite element method by subdividing subdomains for elastodynamic problems

The scaled boundary finite element method(SBFEM) is a semi-analytical numerical method,which models an analysis domain by a small number of large-sized subdomains and discretises subdomain boundaries only.In a subdomain,all fields of state variables including displacement,stress,velocity and acceleration are semi-analytical,and the kinetic energy,strain energy and energy error are all integrated semi-analytically.These advantages are taken in this study to develop a posteriori h-hierarchical adaptive SBFEM for transient elastodynamic problems using a mesh refinement procedure which subdivides subdomains.Because only a small number of subdomains are subdivided,mesh refinement is very simple and efficient,and mesh mapping to transfer state variables from an old mesh to a new one is also very simple but accurate.Two 2D examples with stress wave propagation were modelled.The results show that the developed method is capable of capturing propagation of steep stress regions and calculating accurate dynamic responses,using only a fraction of degrees of freedom required by adaptive finite element method.

Stress boundary layers in the viscoelastic flow past a cylinder in a channel:limiting solutions

The flow past a cylinder in a channel with the aspect ratio of 2 ： 1 for the upper convected Maxwell （UCM） fluid and the Oldroyd-B fluid with the viscosity ratio of 0.59 is studied by using the Galerkin/Least-square finite element method and a p-adaptive refinement algorithm. A posteriori error estimation indicates that the stress-gradient error dominates the total error. As the Deborah number, De, approaches 0.8 for the UCM fluid and 0.9 for the Oldroyd-B fluid, strong stress boundary layers near the rear stagnation point are forming, which are characterized by jumps of the stress-profiles on the cylinder wall and plane of symmetry, huge stress gradients and rapid decay of the gradients across narrow thicknesses. The origin of the huge stress-gradients can be traced to the purely elongational flow behind the rear stagnation point, where the position at which the elongation rate is of 1/2De approaches the rear stagnation point as the Deborah number approaches the critical values. These observations imply that the cylinder problem for the UCM and Oldroyd-B fluids may have physical limiting Deborah numbers of 0.8 and 0.9, respectively.

ON ADAPTIVE WAVELET BOUNDARY ELEMENT METHODS

The present article is concerned with the numerical solution of boundary integral e- quations by an adaptive wavelet boundary element method. This method approximates the solution with a computational complexity that is proportional to the solution＇s best N-term approximation. The focus of this article is on algorithmic issues which includes the crucial building blocks and details about the efficient implementation. By numerical examples for the Laplace equation and the Helmholtz equation, solved for different geome- tries and right-hand sides, we validate the feasibility and efficiency of the adaptive wavelet boundary element method.

An Improved r-Adaptive Galerkin Boundary Element Method Based on Unbalanced Haar Wavelets

An r-adaptive boundary element method（BEM） based on unbalanced Haar wavelets（UBHWs） is developed for solving 2D Laplace equations in which the Galerkin method is used to discretize boundary integral equations.To accelerate the convergence of the adaptive process,the grading function and optimization iteration methods are successively employed.Numerical results of two representative examples clearly show that,first,the combined iteration method can accelerate the convergence;moreover,by using UBHWs,the memory usage for storing the system matrix of the r-adaptive BEM can be reduced by a factor of about 100 for problems with more than 15 thousand unknowns,while the error and convergence property of the original BEM can be retained.

面向双层插值边界面法的非结构自动网格划分

针对数值模拟前处理过程中网格划分存在的困难,提出一种面向双层插值边界面法的非结构自动网格划分方法 .该方法基于网格尺寸、表面曲率、实体厚度等几何特征进行体二叉树自适应细分,避免使用任何协调过渡模板处理悬挂点,降低网格划分的困难.构建了体网格拓扑元素与实体模型边界的快速求交算法,有效提升求交计算效率,降低算法实现复杂度.实验结果表明,最终网格划分实现整体以六面体网格为主,实体边界附近的部分网格以四面体、三棱柱或金字塔网格为辅的非结构自动网格划分,验证了该方法的准确性、有效性及鲁棒性.

基于截断型自适应交叉近似和奇异值分解的涡流无损检测模型

探讨了一种高效的三维涡流无损检测求解模型。该模型首次使用截断型自适应交叉算法和奇异值分解算法加速基于边界元法的涡流无损检测模型。该模型使用没有低频崩溃问题的Stratton‐Chu方程作为边界积分方程,然后使用Rao‐Wilton‐Glisson矢量基函数和脉冲基函数分别将等效面电流、磁流和磁场法向分量展开,通过Galerkin方法测试,得到阻抗矩阵。借助八叉树结构,根据块与块之间的距离关系将阻抗矩阵分为对角块、近区块和远区块,其中对角块和近区块使用边界元法直接计算存储,远区块通过综合运用自适应交叉算法、奇异值分解算法和截断核函数算法进行压缩存储。最后,以涡流无损检测基准问题为例,将运用该方法预测的结果与其他模型预测的结果以及实验结果相比较,验证了所提求解模型的准确性和有效性。

Adaptive mesh refinement immersed boundary method for simulations of laminar flows past a moving thin elastic structure

One of the critical issues in numerical simulation of fluid-structure interaction problems is inaccuracy of the solutions,especially for flows past a stationary thin elastic structure where large deformations occur.High resolution is required to capture the flow characteristics near the fluid-structure interface to enhance accuracy of the solutions within proximity of the thin deformable body.Hence,in this work,an algorithm is developed to simulate fluid-structure interactions of moving deformable structures with very thin thicknesses.In this algorithm,adaptive mesh refinement(AMR)is integrated with immersed boundary finite element method(IBFEM)with two-stage pressure-velocity corrections.Despite successive interpolation of the flow field by IBM,the governing equations were solved using a fixed structured mesh,which significantly reduces the computational time associated with mesh reconstruction.The cut-cell IBM is used to predict the body forces while FEM is used to predict deformation of the thin elastic structure in order to integrate the motions of the fluid and solid at the interface.AMR is used to discretize the governing equations and obtain solutions that efficiently capture the thin boundary layer at the fluid-solid interface.The AMR-IBFEM algorithm is first verified by comparing the drag coefficient,lift coefficient,and Strouhal number for a benchmark case(laminar flow past a circular cylinder at Re=100)and the results showed good agreement with those of other researchers.The algorithm is then used to simulate 2-D laminar flows past stationary and moving thin structures positioned perpendicular to the freestream direction.The results also showed good agreement with those obtained from the arbitrary Lagrangian-Eulerian(ALE)algorithm for elastic thin boundaries.It is concluded that the AMR-IBFEM algorithm is capable of predicting the characteristics of laminar flow past an elastic structure with acceptable accuracy(error of-0.02%)with only-1%of the computational time for simulations with full mesh refinement.

Numerical Solution of Acoustic Scattering by an Adaptive DtN Finite Element Method

Consider the acoustic wave scattering by an impenetrable obstacle in two dimensions,where the wave propagation is governed by the Helmholtz equation.The scattering problem is modeled as a boundary value problem over a bounded domain.Based on the Dirichlet-to-Neumann(DtN)operator,a transparent boundary condition is introduced on an artificial circular boundary enclosing the obstacle.An adaptive finite element based on a posterior error estimate is presented to solve the boundary value problem with a nonlocal DtN boundary condition.Numerical experiments are included to compare with the perfectly matched layer(PML)method to illustrate the competitive behavior of the proposed adaptive method.

栅格法三维六面体网格自动生成算法与优化

提出了以栅格法六面体网格生成为基础方法,基于实体模型几何特征的六面体网格自适应生成算法,首先对模型进行识别,根据实体模型几何特征建立加密源点信息场,并进行相容性控制,采用栅格法生成核心网格,然后进行核心网格与模型边界的拟合,为克服该方法在实体模型表面网格质量较差的缺点,采用节点位置平滑和拓扑关系优化对网格质量进行优化,生成质量较高的六面体网格。网格划分实例表明,该方法实用性强,效果良好。

平面有限元网格生成的自适应技术

在Watson逐点插入算法的基础上发展了边界自适应和约束结点；巨离自适应技术。与以往的方法相比，该方法不但提高了网格生成的自动化程度，而且使生成的单元数量有所减少。实例表明，该算法对于具有任意边界和任意的未结点的平面区域，能在最少的人工干预下获得满意的网格划分结果。

基于自适应交叉逼近技术的边界元法在3维静电场中的应用

常规边界元法(boundary element method,BEM)因形成的方程矩阵稠密非对称而难以应用于大规模问题,BEM矩阵的存储限制了BEM的工程应用。该文介绍了递阶矩阵(hierarchical matrix,H-matrix)的基本概念,并引入了一种新颖的H-matrix压缩技术:自适应交叉逼近(adaptive cross approximation,ACA)。通过对普法BEM的节点根据拓扑结构重新分区和编号,可以将方程矩阵分解为若干具有递阶特性的子矩阵,应用自适应交叉逼近技术将这些子矩阵进行低秩分解可大大降低BEM矩阵对内存的消耗。为了对基于ACA技术的BEM内存消耗和有效性进行验证,建立了三维球形电极模型,通过与普通BEM比较,证实了该文方法可显著减小边界元法的内存使用,并验证了该方法的有效性。