Coupling volume-of-fluid based interface reconstructions with the extended finite element method

We examine the coupling of the patterned-interface-reconstruction (PIR) algorithm with the extended finite element method (X-FEM) for general multi-material problems over structured and unstructured meshes. The coupled method offers the advantages of allowing for local, element-based reconstructions of the interface, and facilitates the imposition of discrete conservation laws. Of particular note is the use of an interface representation that is volume-of-fluid based, giving rise to a segmented interface representation that is not continuous across element boundaries. In conjunction with such a representation, we employ enrichment with the ridge function for treating material interfaces and an analog to Heaviside enrichment for treating free surfaces. We examine a series of benchmark problems that quantify the convergence aspects of the coupled method and examine the sensitivity to noise in the interface reconstruction. The fidelity of a remapping strategy is also examined for a moving interface problem.     

机器人全局路径规划的混合蚁群系统算法

针对蚁群算法易陷入局部最优的缺点以及收敛速度与局部最优的矛盾,提出一种求解移动机器人全局路径规划的改进混合蚁群系统算法。该算法由两部分组成：Dijkstra算法用于规划出一条次优路径;进一步用改进的蚁群系统算法优化次优路径以获得最优路径。在改进的蚁群系统算法中,首先定义了一种新的启发信息函数来增加种群多样性;然后给出改进的交叉算子避免算法陷入局部最优,并进一步提高解的质量。仿真结果表明：所提出的算法与参考文献中的算法相比搜索效率更高,解的质量更好,性能更优。即使在障碍物复杂的环境中,对于多目标点问题,该算法仍能规划出较好的目标遍历路径,且用时时间较少。     

求解带有间断系数泊松方程的修正有限体积

利用修正的有限体积方法求解带有间断系数的泊松方程,改进是对基于笛卡尔坐标系下的调和平均系数进行的。数值实验表明新格式二阶逐点收敛并且在界面处具有二阶精度,新方法较已有的求解不连续扩散系数的算术平均法和调和平均法,特别是在系数跳跃较大的情况下更具优势。     

Simulation of floating bodies with the lattice Boltzmann method

This paper is devoted to the simulation of floating rigid bodies in free surface flows. For that, a lattice Boltzmann based model for liquid–gas–solid flows is presented. The approach is built upon previous work for the simulation of liquid–solid particle suspensions on the one hand, and on an interface-capturing technique for liquid–gas free surface flows on the other. The incompressible liquid flow is approximated by a lattice Boltzmann scheme, while the dynamics of the compressible gas are neglected. We show how the particle model and the interface capturing technique can be combined by a novel set of dynamic cell conversion rules. We also evaluate the behaviour of the free surface–particle interaction in simulations. One test case is the rotational stability of non-spherical rigid bodies floating on a plane water surface–a classical hydrostatic problem known from naval architecture. We show the consistency of our method in this kind of flows and obtain convergence towards the ideal solution for the heeling stability of a floating box.     

A Review and Study on Ritz Method Admissible Functions with Emphasis on Buckling and Free Vibration of Isotropic and Anisotropic Beams and Plates

The first goal of this work is to present a literature review regarding the use of several sets of admissible functions in the Ritz method. The papers reviewed deal mainly with the analysis of buckling and free vibration of isotropic and anisotropic beams and plates. Theoretically, in order to obtain a correct solution, the set of admissible functions must not violate the essential or geometric boundary conditions and should also be linearly independent and complete. However, in practice, some of the sets of functions proposed in the literature present a bad numerical behavior, namely in terms of convergence, computational time and stability. Thus, a second goal of the present work is to compare the performance of several sets of functions in terms of these three features. To achieve this objective, the free vibration analysis of a fully clamped rectangular plate is carried out using six different sets of functions, along with the study of the convergence of natural frequencies and mode shapes, the computational time and the numerical stability.     

A Strongly Conservative Hybrid DG/Mixed FEM for the Coupling of Stokes and Darcy Flow

We consider the coupling of free and porous media flow governed by Stokes and Darcy equations with the Beavers–Joseph–Saffman interface condition. This model is discretized using a divergence-conforming finite element for the velocities in the whole domain. Hybrid discontinuous Galerkin techniques and mixed methods are used in the Stokes and Darcy subdomains, respectively. The discretization achieves mass conservation in the sense of \(H(\mathrm {div},\Omega )\), and we obtain optimal velocity convergence. Numerical results are presented to validate the theoretical findings.     

The falkneer-skan equation: Numerical solutions within group invariance theory

The iterative transformation method, defined within the framework of the group invariance theory, is applied to the numerical solution of the Falkner-Skan equation with relevant boundary conditions. In this problem a boundary condition at infinity is imposed which is not suitable for a numerical use. In order to overcome this difficulty we introduce a free boundary formulation of the problem, and we define the iterative transformation method that reducess the free boundary formulation to a sequence of initial value problems. Moreover, as far as the value of the wall shear stress is concerned we propose a numerical test of convergence. The usefulness of our approach is illustrated by considering the wall shear stress for the classical Homann and Hiemenz flows. In the Homann's case we apply the proposed numerical test of convergence, and meaningful numerical results are listed. Moreover, for both cases we compared our results with those reported in literature.     

Numerical solution of hereditary control problems using necessary conditions

A centered difference method for the boundary value problems arising as necessary conditions for hereditary control problems is given. Convergence and convergence rates are established and numerical examples are presented and compared with other results in the literature.     

A Finite Difference Method and Analysis for 2D Nonlinear Poisson–Boltzmann Equations

A fast finite difference method based on the monotone iterative method and the fast Poisson solver on irregular domains for a 2D nonlinear Poisson–Boltzmann equation is proposed and analyzed in this paper. Each iteration of the monotone method involves the solution of a linear equation in an exterior domain with an arbitrary interior boundary. A fast immersed interface method for generalized Helmholtz equations on exterior irregular domains is used to solve the linear equation. The monotone iterative method leads to a sequence which converges monotonically from either above or below to a unique solution of the problem. This monotone convergence guarantees the existence and uniqueness of a solution as well as the convergence of the finite difference solution to the continuous solution. A comparison of the numerical results against the exact solution in an example indicates that our method is second order accurate. We also compare our results with available data in the literature to validate the numerical method. Our method is efficient in terms of accuracy, speed, and flexibility in dealing with the geometry of the domain     

The dynamic stresses induced by moving interfacial cracks

Elastodynamic problems involving moving mixed boundary conditions are considered. In particular, uniform and nonuniform propagation in Mode I, II and III types of motion of semi-infinite cracks along the interface of two dissimilar half-spaces are treated. The equations of motion are transformed to a new coordinate system in which the moving tip of the crack appears always at the origin of the coordinates. An implicit three-level numerical method of solution is given which is proved to be more efficient than a previous explicit one. Furthermore, an implicit method for the numerical formulation of the boundary conditions is presented and is shown to yield better results than a previous formulation. The stability analysis of the proposed finite difference approximation is given, and stability criteria are presented as well as a proof of the convergence of the iterative process involved in the numerical formulation of the boundary and interface conditions. The reliability of the present method of solution is examined in several situations where analytical results are known.     

Fourth-order derivative-free methods for solving non-linear equations

Two new one-parameter families of methods for finding simple and real roots of non-linear equations without employing derivatives of any order are developed. Error analysis providing the fourth-order convergence is given. Each member of the families requires three evaluations of function per step, and therefore the method has an efficiency index of 1.587. Numerical examples are presented and the performance of the method presented here is compared with methods available in the literature.     

Uniform Convergent Tailored Finite Point Method for Advection–Diffusion Equation with Discontinuous,Anisotropic and Vanishing Diffusivity

We propose two tailored finite point methods for the advection–diffusion equation with anisotropic tensor diffusivity. The diffusion coefficient can be very small in one direction in some part of the domain and be discontinuous at the interfaces. When flows advect from the vanishing-diffusivity region towards the non-vanishing diffusivity region, standard numerical schemes tend to cause spurious oscillations or negative values. Our proposed schemes have uniform convergence in the vanishing diffusivity limit, even when the solution exhibits interface and boundary layers. When the diffusivity is along the coordinates, the positivity and maximum principle can be proved. We use the value as well as their derivatives at the grid points to construct the scheme for nonaligned case, which makes it can achieve good accuracy and convergence for the derivatives as well, even when there exhibit boundary or interface layers. Numerical experiments are presented to show the performance of the proposed scheme.     

Jacobi–Ritz method for free vibration analysis of uniform and stepped circular cylindrical shells with arbitrary boundary conditions: A unified formulation

A semi analytical approach is employed to analyze free vibration characteristics of uniform and stepped circular cylindrical shells subject to arbitrary boundary conditions. The analytical model is established on the basis of multi-segment partitioning strategy and Flügge thin shell theory. The admissible displacement functions are handled by unified Jacobi polynomials and Fourier series. In order to obtain continuous conditions and satisfy arbitrary boundary conditions, the penalty method about the spring technique is adopted. The solutions about free vibration behavior of circular cylindrical shells were obtained by approach of Rayleigh–Ritz. To confirm the reliability and accuracy of this method, convergence study and numerical verifications for circular cylindrical shells subject to different boundary conditions, Jacobi parameters, spring parameters and maximum degree of permissible displacement function are carried out. Through comparative analyses, it is obvious that the present method has a good stable and rapid convergence property and the results of this paper agree closely with the published literature. In addition, some interesting results about the geometric dimensions are investigated.     

Variational Dynamics of Free Triple Junctions

We propose a level set framework for representing triple junctions either with or without free endpoints. For triple junctions without free endpoints, our method uses two level set functions to represent the three segments that constitute the structure. For free triple junctions, we extend our method using the free curve work of Schaeffer and Vese (J Math Imaging Vis, 1–17, 2013), Smereka (Phys D Nonlinear Phenom 138(3–4):282–301, 2000). For curves moving under length minimizing flows, it is well known that the endpoints either intersect perpendicularly to the boundary, do not intersect the boundary of the domain or the curve itself (free endpoints), or meet at triple junctions. Although many of these cases can be formulated within the level set framework, the case of free triple junctions does not appear in the literature. Therefore, the proposed free triple junction formulation completes the important curve structure representations within the level set framework. We derive an evolution equation for the dynamics of the triple junction under length and area minimizing flow. The resulting system of partial differential equations are both coupled and highly non-linear, so the system is solved numerically using the Sobolev preconditioned descent. Qualitative numerical experiments are presented on various triple junction and free triple junction configurations, as well as an example with a quadruple junction instability. Quantitative results show convergence of the preconditioned algorithm to the correct solutions.     

An improved interface element with variable nodes for non-matching finite element meshes

Extensive improvements of the interface element method (IEM) are proposed for the efficient treatment of non-matching finite element meshes. Our approach enables us to establish the master element via the moving least-square (MLS) approximation, and so to remove the cumbersome process of constructing interface elements. The values of shape functions and their derivatives are therefore mapped from the master element, as in the conventional finite element method. For the assurance of convergence and compatibility condition, a patch test is demonstrated. Through several examples of 2D linear elasticity, the convergence rate is compared between the present interface element and the previous version.     

An efficient block parallel AMR method for two phase interfacial flow simulations

The direct numerical simulation of two phase interfacial flows can be computationally challenging, as the strong resolution needed to follow the deformations of the interface leads to a lot of time spent solving the whole computation domain. Efficient solution of such problems requires an adaptive mesh refinement capability to concentrate computational effort where it is most needed. In this paper a parallel adaptive algorithm to solve incompressible two-phase flows with surface tension is presented: the AMR is handled with the help of the PARAMESH package. The free interface between fluids is tracked via Level Set approach; the jump conditions at the interface for pressure and velocity are imposed by the Ghost Fluid method. A multigrid preconditioned BiCG-stab solver adapted to the AMR data structure has been developed to allow high density ratio computations (up to 1:1000). Special treatment has been done at the refinement jumps to maintain the fine mesh accuracy. Computational results are compared in different test cases with analytical solutions or literature, and show very good agreement with the references. The effectiveness of PARAMESH parallelization has been quite well maintained, as shown in the strong and weak scaling tests. Speed-up capabilities of the AMR are demonstrated.     

A decoupled scheme with leap-frog multi-time step for non-stationary Stokes–Darcy system

In this paper, a multiple-time-step decoupled algorithm for a non-stationary Stokes–Darcy problem is proposed and investigated. Under a modest time step restriction of physical parameters and the time step proportion, we give the stability analysis and convergence analysis of the decoupled scheme with different time step in fluid and porous subregions. Finally, a series of numerical experiments are provided to illustrate the accuracy, efficiency, and stability of the presented method for the coupled problem with the Beavers–Joseph–Saffman–Jones interface conditions.     

A numerical method for the simulation of free surface flows with surface tension

A numerical model for the simulation of three-dimensional liquid–gas flows with free surfaces and surface tension is presented. The incompressible Navier–Stokes equations are assumed to hold in the liquid domain, while the gas pressure is assumed to be constant in each connected component of the gas domain and to follow the ideal gas law. The surface tension effects are imposed as a normal force on the interface.

An implicit splitting scheme is used to decouple the physical phenomena. Given the curvature of the liquid–gas interface, the method described in [Caboussat A, Picasso M, Rappaz J. Numerical simulation of free surface incompressible liquid flows surrounded by compressible gas. J Comput Phys 2005;203(2):626–49] is used to track the liquid domain and compute the velocity and pressure in the liquid and the pressure in the gas domain. Then the surface tension effects are added. A variational method for the computation of the curvature is presented by smoothing the characteristic function of the liquid domain and using a finite element unstructured mesh.

The model is validated and numerical results in two and three space dimensions are presented for bubbles and/or droplets flows.     

用MCIWnd实现视频的灵活播放

视频剪辑播放可以通过ＭＣＩ接口很容易的实现，但界面呆板，灵活性差，为使视频剪辑播放灵活，使用ＭＣＩＷｎｄ接口，效果很好。文中介绍了其功能、控制、实例与实现。     

一种基于路由协议的拥塞控制策略

提出了一种基于OSPF路由协议的拥塞控制策略。利用OSPF协议的链路状态更新报文（LSA）中的空闲位,增加路由器的拥塞状态和流量状态的描述,随LSA报文的传播将路由器的拥塞情况告知其他路由器,利用OSPF的快速收敛及时得知网络拥塞状况并进行早期的拥塞避免。仿真模拟表明,该方案能够控制网络拥塞,减小延迟,达到网络负载平衡。