Computation of Hele-Shaw flows with free boundaries

A novel method for calculation of Hele-Shaw flows with receding free boundaries is presented. The method is applied to flows with suction from a point sink and to flow in a channel with parallel walls. In each case the unknown fluid region is mapped conformally onto the unit disc, the free boundary being mapped onto the unit circle. This mapping, which is a function of position and time, is calculated numerically at points on the unit circle using a version of the boundary integral method. The free boundary is thus found without explicit calculation of the pressure at internal points, and the computation times are much less than those for other numerical methods for this problem. Numerical results are compared with explicit analytic solutions for several test problems.     

Lagrangian boundary condition and non-linear propagation as causes of Gaussian noise spectrum deformation

In this paper a novel analytical method of spectral analysis for acoustic Gaussian noise signals propagated in lossless fluids is presented. The starting point for theoretical considerations is the “input” signal transformation given by Earnshaw's parametric solution. By using a method of parameter elimination, based upon the filtering property of the delta function and its spectral representation, and utilizing a new theorem concerning continuous stochastic processes, an integral formula which allows one to map the power spectrum of the input signal (i.e., the boundary condition of Lagrange or the boundary condition of Euler) into the power spectrum of the particle velocity for an arbitrary point of the acoustic field (before the shock formation), is derived. The final formulae are well-adapted to numerical calculations of “output” spectra by electronic means.     

A spectral fictitious domain method with internal forcing for solving elliptic PDEs

A fictitious domain method is presented for solving elliptic partial differential equations using Galerkin spectral approximation. The fictitious domain approach consists in immersing the original domain into a larger and geometrically simpler one in order to avoid the use of boundary fitted or unstructured meshes. In the present study, boundary constraints are enforced using Lagrange multipliers and the novel aspect is that the Lagrange multipliers are associated with smooth forcing functions, compactly supported inside the fictitious domain. This allows the accuracy of the spectral method to be preserved, unlike the classical discrete Lagrange multipliers method, in which the forcing is defined on the boundaries. In order to have a robust and efficient method, equations for the Lagrange multipliers are solved directly with an influence matrix technique. Using a Fourier–Chebyshev approximation, the high-order accuracy of the method is demonstrated on one- and two-dimensional elliptic problems of second- and fourth-order. The principle of the method is general and can be applied to solve elliptic problems using any high order variational approximation.     

Convective scheme solution of the Boltzmann transport equation for nanoscale semiconductor devices

A model for the simulation of the electron energy distribution in nanoscale metal–oxide–semiconductor field-effect transistor (MOSFET) devices, using a kinetic simulation technique, is implemented. The convective scheme (CS), a method of characteristics, is an accurate method of solving the Boltzmann transport equation, a nonlinear integrodifferential equation, for the distribution of electrons in a MOSFET device. The method is used to find probabilities for use in an iterative scheme which iterates to find collision rates in cells. The CS is also a novel approach to 2D semiconductor device simulation. The CS has been extended to handle boundary conditions in 2D as well as to calculation of polygon overlap for polygons of more than three sides. Electron energy distributions in the channel of a MOSFET are presented.     

A modified Fourier series solution for vibration analysis of truncated conical shells with general boundary conditions

Free vibration analysis of truncated conical shells with general elastic boundary conditions is presented in this paper. An accurate modified Fourier series solution is developed, in which, regardless of the boundary conditions, each displacement of the conical shell is invariantly expressed as a new form of improved series expansions composed of a standard Fourier series and closed-form auxiliary functions introduced to ensure and accelerate the convergence of the series expansion. All the expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh–Ritz method. By using the present method, conical shells with arbitrary boundary conditions including all classical and elastic end restraints can be solved in a unified form. The accuracy and convergence of the current approach are validated by numerical examples and comparison with FEM results and those from the literature, and excellent accuracy is demonstrated. Comprehensive studies on the effects of elastic restraint parameters, semi-vertex angle and the ratio of length to radius are also reported. Some new results are presented for cases with elastic boundary restraints which may serve as benchmark solution for future researches.     

Convective scheme solution of the Boltzmann transport equation for nanoscale semiconductor devices

A model for the simulation of the electron energy distribution in nanoscale metal–oxide–semiconductor field-effect transistor (MOSFET) devices, using a kinetic simulation technique, is implemented. The convective scheme (CS), a method of characteristics, is an accurate method of solving the Boltzmann transport equation, a nonlinear integrodifferential equation, for the distribution of electrons in a MOSFET device. The method is used to find probabilities for use in an iterative scheme which iterates to find collision rates in cells. The CS is also a novel approach to 2D semiconductor device simulation. The CS has been extended to handle boundary conditions in 2D as well as to calculation of polygon overlap for polygons of more than three sides. Electron energy distributions in the channel of a MOSFET are presented.     

基于倒置结构的直接体积重建

通过多个点状探测器在三维空间中的适当分布的排列,得到了基于倒置结构Ｘ射线锥形束投影的直接体积重建三维成像七锥形束边界重建相结合,针对倒置结构构造的重建算法及其数值仿真表明,新的成像模式相对于传统的锥形束边界重建,在实际存在Ｘ射线投影噪声情形下有明显的优点。     

复杂背景下钢索图像的纹理分割与边界识别

 针对复杂背景下钢索图像难以准确分割的问题,提出一种基于纹理分析的钢索图像分割与边界识别方法.采用基于模糊Hough变换的纹理方向检测方法确定钢索走向,利用边缘方向密度直方图作为纹理特征,对与钢索纹理方向相应的边缘方向赋予不同权重,抑制纹理分割中背景的干扰,对钢丝绳图像进行聚类分割,采用检测平行直线的方法确定其边界,并根据算法参量对边界进行修正.在实验中,对比了边缘方向密度直方图特征与灰度共生矩阵、局部二值模式在钢索图像纹理分割中的结果与计算时间,结果表明边缘方向密度直方图特征计算速度快、受背景干扰小,分割准确率高.本文方法无须预先训练,受背景干扰小,可以准确地识别出钢索并确定其边界,能满足钢丝绳视觉检测的要求.     

一种模拟倾斜折射率界面光波导的新方法

针对传统离散格式下，束传播方法(BPM)模拟倾斜折射率界面出现的问题，提出了一种简明且易于编程实现的改进方案. 在横向上，通过坐标系变换和插值处理，以新颖的7点差分格式代替传统的5点差分方式；在纵向上，以四阶显式Runge-Kutta方法(RKBPM)代替二阶Crank-Nicholson算法(CNBPM)，避免了求解不规则矩阵方程，从而使计算效率显著提高. 关键词： 束传播方法 Runge-Kutta方法 光波导 脊形波导     

Extraction of isotropic points using simulated isoclinics obtained by photoelasticity-assisted finite element analysis

A method for extracting isotropic points in structures using simulated isoclinics obtained from a combination of photoelastic experiments and finite element analysis (FEA) is presented. This method is divided into two parts. The first part involves the confirmation of the boundary condition necessary for FEA using isochromatics obtained by photoelastic experiments. The second part involves the determination of isotropic points using simulated isoclinics obtained by FEA under the boundary condition confirmed by photoelastic experiments. This method is applied to a ring and T-shaped plates subjected to a compressive load. The results show that the isotropic points in the ring and T-shaped plates could be accurately and easily extracted by this method.     

A temperature-related boundary Cauchy–Born method for multi-scale modeling of silicon nano-structures

The surface, edge and corner effects have significant influences in the electrical and optical properties of silicon nano-structures. In this paper, a novel hierarchical temperature-related multi-scale model is presented based on the boundary Cauchy–Born method to investigate not only the surface but also the edge and corner effects in thermal properties of diamond-like structures such as silicon nano-structures at finite temperature. A combined finite element method and molecular dynamics are respectively employed in macro- and micro-scale levels. The temperature-related Cauchy–Born rule is applied using the Helmholtz free energy, as the energy density of equivalent continua relating to the Tersoff inter-atomic potential. The model employs radial quadratures at the surface, edge and corner elements as an indicator of material behavior. The capability of computational algorithm is illustrated by numerical simulation of a nano-scale cube at finite temperature and the results are compared with the atomistic model.     

Towards a quantal dynamical simulation of the neutron star’s crust

We present a novel method to study the dynamics of bulk fermion systems such as the neutron star’s crust. By introducing periodic boundary conditions into Fermionic Molecular Dynamics, it becomes possible to examine the long-range many-body correlations induced by antisymmetrisation in bulk fermion systems. The presented technique treats the spins and the fermionic nature of the nucleons explicitly and permits investigating the dynamics of the system. Despite the increased complexity related to the periodic boundary conditions, the proposed formalism remains computationally feasible.     

Free vibration of composite membranes with arbitrary shape

This paper is concerned with a method for solving problems of a composite membrane with an arbitrarily shaped outer boundary and an arbitrarily shaped inner boundary. The boundary conditions and the conditions of continuity are satisfied directly by using a Fourier expansion collocation method which has been given by Nagaya. The general equation for finding the natural frequencies of the composite membranes has been presented. As examples, numerical calculations have been carried out for composite polygonal membranes, composite elliptical membranes and composite circular membranes with eccentric circular boundaries.     

A representation of curved boundaries for the solution of the Navier–Stokes equations on a staggered three-dimensional Cartesian grid

A method is presented for representing curved boundaries for the solution of the Navier–Stokes equations on a non-uniform, staggered, three-dimensional Cartesian grid. The approach involves truncating the Cartesian cells at the boundary surface to create new cells which conform to the shape of the surface. We discuss in some detail the problems unique to the development of a cut cell method on a staggered grid. Methods for calculating the fluxes through the boundary cell faces, for representing pressure forces and for calculating the wall shear stress are derived and it is verified that the new scheme retains second-order accuracy in space. In addition, a novel “cell-linking” method is developed which overcomes problems associated with the creation of small cells while avoiding the complexities involved with other cell-merging approaches. Techniques are presented for generating the geometric information required for the scheme based on the representation of the boundaries as quadric surfaces. The new method is tested for flow through a channel placed oblique to the grid and flow past a cylinder at Re=40 and is shown to give significant improvement over a staircase boundary formulation. Finally, it is used to calculate unsteady flow past a hemispheric protuberance on a plate at a Reynolds number of 800. Good agreement is obtained with experimental results for this flow.     

An adaptive version of ghost-cell immersed boundary method for incompressible flows with complex stationary and moving boundaries

An adaptive version of immersed boundary method for simulating flows with complex stationary and moving boundaries is presented.The method employs a ghost-cell methodology which allows for a sharp representation of the immersed boundary.To simplify the implementation of the methodology,a volume-of-fluid method is introduced to identify the immersed boundary.In addition,the domain is spatially discretized using a tree-based discretization which is relatively simple to implement a fully flexible adaptive refi...     

Inverse scattering by a continuation method with initial guesses from a direct imaging algorithm

A novel continuation method is presented for solving the inverse medium scattering problem of the Helmholtz equation, which is to reconstruct the shape of the inhomogeneous medium from boundary measurements of the scattered field. The boundary data is assumed to be available at multiple frequencies. Initial guesses are chosen from a direct imaging algorithm, multiple signal classification (MUSIC), along with a level set representation at a certain wavenumber, where the Born approximation may not be valid. Each update via recursive linearization on the wavenumbers is obtained by solving one forward and one adjoint problem of the Helmholtz equation.     

Binary granular gas mixtures: Theory,layering effects and some open questions

A theory of dilute binary granular gas mixtures comprising smooth spheres, which is formally valid for all physical values of the pertinent coefficients of restitution, is presented. Constitutive relations are obtained using the Chapman Enskog procedure, in the framework of which relatively high orders in the Sonine polynomial expansion are employed. The latter is made possible by a computer-aided method. The transport coefficients are shown to converge as a function of the number of Sonine polynomials employed, typically requiring 3 polynomials, but in some cases up to 6 polynomials are required for convergence to within 1%. A comparison with results obtained using the Grad method helps reveal the limitations of the Chapman-Enskog expansion. In particular, in some cases both the Chapman Enskog expansion and the Grad method give unphysical results, though they agree with each other. These issues are related to the lack of scale separation in granular gases. Using the constitutive relations we obtain a novel segregation pattern in vertically vibrated granular mixtures, which comprises up to five layers; this is an extension of a previously obtained three-layer configuration. Finally, the question of effective hydrodynamic boundary conditions at the transition to the Knudsen regime is discussed: in particular, it seems that in some cases the boundary condition for the heat flux in the hydrodynamic regime is “unphysical”.     

A basic study on the sound field analysis of periodic structures by boundary integral equation method

This study deals with the development of the approximate method to analyze the sound field around equally spaced finite obstacles, using the periodic boundary condition. First, on the assumption that the equally spaced finite obstacles are the periodically arranged obstacles, the sound field is analyzed by boundary integral equation method with a Green’s function which satisfies the periodic boundary condition. Furthermore, by comparing these results and the exact solution by using the fundamental solution as Green’s function, the validity of the approximate method is also investigated. Next, in order to evaluate the applicability of the approximate method, the simple formula using some parameters, i.e., the frequency, the period, and the number of obstacles, etc., is proposed. The results of the sound field analysis applied the formula are presented.     

Boundary element-free method for elastodynamics

1 Introduction In recent years, more and more attention has been paid to researches on the meshless (or meshfree) method, which makes it a hot direction of computational mechanics[1,2]. The meshless method is the approximation based on nodes, then the large deformation and crack growth problems can be simulated with the method without the re-meshing technique. And the meshless method has some advantages over the traditional computa- tional methods, such as finite element method (FEM) and boun…     

Boundary element-free method for elastodynamics

The moving least-square approximation is discussed first. Sometimes the method can form an ill-conditioned equation system, and thus the solution cannot be obtained correctly. A Hilbert space is presented on which an orthogonal function system mixed a weight function is defined. Next the improved moving least-square approximation is discussed in detail. The improved method has higher computational efficiency and precision than the old method, and cannot form an ill-conditioned equation system. A boundary element-free method (BEFM) for elastodynamics problems is presented by combining the boundary integral equation method for elastodynamics and the improved moving least-square approximation. The boundary element-free method is a meshless method of boundary integral equation and is a direct numerical method compared with others, in which the basic unknowns are the real solutions of the nodal variables and the boundary conditions can be applied easily. The boundary element-free method has a higher computational efficiency and precision. In addition, the numerical procedure of the boundary element-free method for elastodynamics problems is presented in this paper. Finally, some numerical examples are given.