Generalization of the Spline Interpolation Based on the Principle of the Compact Schemes

In this work the authors extend the high order compact difference schemes to the matching technique to develop a Local Matched Reconstruction theory that can be also considered as a generalization of the spline theory. The problem of the high order reconstructions correlated to an optimal matching in overlapping regions for contiguous expansions in one or more dimensions is stressed; some new generalized matched interpolations and their related numerical schemes are presented together with Fourier analysis of errors. Finally, some relevant aspects of the computational efforts associated to the various approaches are discussed.     

High-order Compact Schemes for Nonlinear Dispersive Waves

High-order compact finite difference schemes coupled with high-order low-pass filter and the classical fourth-order Runge–Kutta scheme are applied to simulate nonlinear dispersive wave propagation problems described the Korteweg-de Vries (KdV)-like equations, which involve a third derivative term. Several examples such as KdV equation, and KdV-Burgers equation are presented and the solutions obtained are compared with some other numerical methods. Computational results demonstrate that high-order compact schemes work very well for problems involving a third derivative term.     

High Accuracy Schemes for DNS and Acoustics

High-accuracy schemes have been proposed here to solve computational acoustics and DNS problems. This is made possible for spatial discretization by optimizing explicit and compact differencing procedures that minimize numerical error in the spectral plane. While zero-diffusion nine point explicit scheme has been proposed for the interior, additional high accuracy one-sided stencils have also been developed for ghost cells near the boundary. A new compact scheme has also been proposed for non-periodic problems—obtained by using multivariate optimization technique. Unlike DNS, the magnitude of acoustic solutions are similar to numerical noise and that rules out dissipation that is otherwise introduced via spatial and temporal discretizations. Acoustics problems are wave propagation problems and hence require Dispersion Relation Preservation (DRP) schemes that simultaneously meet high accuracy requirements and keeping numerical and physical dispersion relation identical. Emphasis is on high accuracy than high order for both DNS and acoustics. While higher order implies higher accuracy for spatial discretization, it is shown here not to be the same for time discretization. Specifically it is shown that the 2nd order accurate Adams-Bashforth (AB)—scheme produces unphysical results compared to first order accurate Euler scheme. This occurs, as the AB-scheme introduces a spurious computational mode in addition to the physical mode that apportions to itself a significant part of the initial condition that is subsequently heavily damped. Additionally, AB-scheme has poor DRP property making it a poor method for DNS and acoustics. These issues are highlighted here with the help of a solution for (a) Navier–Stokes equation for the temporal instability problem of flow past a rotating cylinder and (b) the inviscid response of a fluid dynamical system excited by simultaneous application of acoustic, vortical and entropic pulses in an uniform flow. The last problem admits analytic solution for small amplitude pulses and can be used to calibrate different methods for the treatment of non-reflecting boundary conditions as well.     

TVD Fluxes for the High-Order ADER Schemes

In this paper we propose to use a TVD flux, instead of a first-order monotone flux, as the building block for designing very high-order methods; we implement the idea in the context of ADER schemes via a new flux expansion. Systematic assessment of the new schemes shows substantial gains in accuracy; these are particularly evident for problems involving long time evolution     

Application of Compact Schemes to Large Eddy Simulation of Turbulent Jets

We present 3-D large eddy simulation (LES) results for a turbulent Mach 0.9 isothermal round jet at a Reynolds number of 100,000 (based on jet nozzle exit conditions and nozzle diameter). Our LES code is part of a Computational Aeroacoustics (CAA) methodology that couples surface integral acoustics techniques such as Kirchhoff's method and the Ffowcs Williams– Hawkings method with LES for the far field noise estimation of turbulent jets. The LES code employs high-order accurate compact differencing together with implicit spatial filtering and state-of-the-art non-reflecting boundary conditions. A localized dynamic Smagorinsky subgrid-scale (SGS) model is used for representing the effects of the unresolved scales on the resolved scales. A computational grid consisting of 12 million points was used in the present simulation. Mean flow results obtained in our simulation are found to be in very good agreement with the available experimental data of jets at similar flow conditions. Furthermore, the near field data provided by the LES is coupled with the Ffowcs Williams–Hawkings method to compute the far field noise. Far field aeroacoustics results are also presented and comparisons are made with experimental measurements of jets at similar flow conditions. The aeroacoustics results are encouraging and suggest further investigation of the effects of inflow conditions on the jet acoustic field.     

On the Total Variation of High-Order Semi-Discrete Central Schemes for Conservation Laws

We discuss a new fifth-order, semi-discrete, central-upwind scheme for solving one-dimensional systems of conservation laws. This scheme combines a fifth-order WENO reconstruction, a semi-discrete central-upwind numerical flux, and a strong stability preserving Runge–Kutta method. We test our method with various examples, and give particular attention to the evolution of the total variation of the approximations.     

Finite Volume Formulation of Compact Upwind and Central Schemes with Artificial Selective Damping

The present paper describes the use of compact upwind and compact central schemes in a Finite Volume formulation with an extension towards arbitrary meshes. The different schemes are analyzed and tested on several numerical experiments. A new formulation of artificial selective damping that is applicable on non-uniform Cartesian meshes is presented. Results are shown for a 1D advection equation, a 2D rotating Gaussian pulse and a subsonic inviscid vortical flow on uniform and non-uniform meshes and for a non-linear acoustic pulse.     

Compact high-order schemes for the Euler equations

An implicit approximate factorization (AF) algorithm is constructed, which has the following characteristics.

Bounded Error Schemes for the Wave Equation on Complex Domains

This paper considers the application of the method of boundary penalty terms (SAT) to the numerical solution of the wave equation on complex shapes with Dirichlet boundary conditions. A theory is developed, in a semi-discrete setting, that allows the use of a Cartesian grid on complex geometries, yet maintains the order of accuracy with only a linear temporal error-bound. A numerical example, involving the solution of Maxwell’s equations inside a 2-D circular wave-guide demonstrates the efficacy of this method in comparison to others (e.g., the staggered Yee scheme)—we achieve a decrease of two orders of magnitude in the level of the L₂-error.     

Staggered Finite Difference Schemes for Conservation Laws

In this work, we introduce new finite-difference shock-capturing central schemes on staggered grids. Staggered schemes may have better resolution of the corresponding unstaggered schemes of the same order. They are based on high-order nonoscillatory reconstruction (ENO or WENO), and a suitable ODE solver for the computation of the integral of the flux. Although they suffer from a more severe stability restriction, they do not require a numerical flux function. A comparison of the new schemes with high-order finite volume (on staggered and unstaggered grids) and high order unstaggered finite difference methods is reported.     

High Accuracy Compact Schemes and Gibbs' Phenomenon

Compact difference schemes have been investigated for their ability to capture discontinuities. A new proposed scheme (Sengupta, Ganerwal and De (2003). J. Comp. Phys. 192(2), 677.) is compared with another from the literature Zhong (1998). J. Comp. Phys. 144, 622 that was developed for hypersonic transitional flows for their property related to spectral resolution and numerical stability. Solution of the linear convection equation is obtained that requires capturing discontinuities. We have also studied the performance of the new scheme in capturing discontinuous solution for the Burgers equation. A very simple but an effective method is proposed here in early diagnosis for evanescent discontinuities. At the discontinuity, we switch to a third order one-sided stencil, thereby retaining the high accuracy of solution. This produces solution with vastly reduced Gibbs' phenomenon of the solution. The essential causes behind Gibbs' phenomenon is also explained.     

Compact finite volume methods for the diffusion equation

We describe an approach to treating initial-boundary-value problems by finite volume methods in which the parallel between differential and difference arguments is closely maintained. By using intrinsic geometrical properties of the volume elements, we are able to describe discrete versions of the div, curl, and grad operators which lead, using summation-by-parts techniques, to familiar energy equations as well as the div curl=0 and curl grad=0 identities. For the diffusion equation, these operators describe compact schemes whose convergence is assured by the energy equations and which yield both the potential and the flux vector with second-order accuracy. A simplified potential form is especially useful for obtaining numerical results by multigrid and ADI methods. The treatment of general curvilinear coordinates is shown to result from a specialization of these general results.     

一种基于多相带通结构的信道化滤波器算法

针对信道化滤波器要求运算速度快、消耗资源多、难以实时处理的突出问题,从多相滤波器,信道化滤波器的结构、原理和运算效率分析出发,推导了一种基于多相带通结构的信道化滤波器算法模型。这种算法将现有多相结构信道化滤波器模型中的低通设计改为带通设计,实现了复数乘法运算全部集中在带通滤波环节当中,并采用协调分级DFT算法的实现方案,大幅度节省了硬件资源,提高了运算效率,实现了信道化滤波器在通用FP—GA和DSP芯片中的实时处理,硬件仿真结果验证了算法模型的正确性和有效性。     

High Order Fluctuation Schemes on Triangular Meshes

We develop a new class of schemes for the numerical solution of first-order steady conservation laws. The schemes are of the residual distribution, or fluctuation-splitting type. These schemes have mostly been developed in the context of triangular or tetrahedral elements whose degrees of freedom are their nodal values. We work here with more general elements that allow high-order accuracy. We introduce, for an arbitrary number of degrees of freedom, a simple mapping from a low-order monotone scheme to a monotone scheme that is as accurate as the degrees of freedom will allow. Proofs of consistency, convergence and accuracy are presented, and numerical examples from second, third and fourth-order schemes.     

A Note on Two Classical Enhancement Filters and Their Associated PDE's

We establish in 2D, the P.D.E. associated with a classical image enhancement filter, the Kramer operator and compare it with another classical shock filter, the Osher-Rudin filter. We show that each one corresponds to a non-flat mathematical morphology operator conditioned by a the sign of an edge detector. In the case of the Kramer operator, the equation is conditioned by the Canny edge detector while in the case of the original Rudin-Osher filter, the equation is conditioned by the sign of the Laplacian.     

Residual Distribution Schemes on Quadrilateral Meshes

We propose an investigation of the residual distribution schemes for the numerical approximation of two-dimensional hyperbolic systems of conservation laws on general quadrilateral meshes. In comparison to the use of triangular cells, usual basic features are recovered, an extension of the upwinding concept is given, and a Lax–Wendroff type theorem is adapted for consistency. We show how to retrieve many variants of standard first and second-order accurate schemes. They are proven to satisfy this theorem. An important part of this paper is devoted to the validation of these schemes by various numerical tests for scalar equations and the Euler equations system for compressible fluid dynamics on non Cartesian grids. In particular, second-order accuracy is reached by an adaptation of the Linearity preserving property to quadrangle meshes. We discuss several choices as well as the convergence of iterative method to steady state. We also provide examples of schemes that are not constructed from an upwinding principle     

基于抽样和Bloom Filters的长流检测

长流检测对网络检测和管理有着重要的意义.提出一种基于抽样和Bloom Filters的长流检测算法,首先对报文进行抽样,然后通过Bloom Filters哈希运算,在内存中用临时表和流信息表来判断到达阈值的流并维护其信息,满足了高速网络环境下长流检测的要求,在保证测量精度的同时有效得控制了资源消耗.实验分析表明,和已有的方法相比,具有简单易行、资源可控等优点.     

Numerical Schemes of Shock Filter Models for Image Enhancement and Restoration

Considerable interest has recently been given to signal processing models based on partial differential equations. Successively improved models based on hyperbolic partial differential equation types are proposed in the literature. These models yield interesting results; however, it would be of great interest to generalize them in order to increase their efficiency. In this paper, we propose a generalized shock filter model for one-dimensional signal restoration. After justifying the existence and uniqueness of the solutions in an adequate vector space, we propose an effective numerical scheme to discretize the proposed model, and derive a two-dimensional numerical scheme directly from the one-dimensional model following a space-split strategy. We then prove a stability result for both schemes. We conclude our study by providing high-quality experimental results for one- and two-dimensional signal enhancement and restoration, and showing the influence the shock speed control has on processing time.     

车载自组网Sybil攻击检测方案研究综述

在车载自组网中,Sybil攻击是指恶意车辆通过伪造、偷窃或合谋等非法方式获取虚假身份并利用多个身份进行非正常行为而威胁到其他驾乘者生命财产安全的一种攻击。介绍了车载自组网中Sybil攻击的起因与危害,对Sybil攻击的检测方案进行了论述。根据检测过程是否与位置相关,将Sybil攻击检测方案分为与位置无关的检测方案和与位置有关的检测方案两类,对其中的检测方案进行了分类和比较。最后指出了现有方案中存在的问题和未来可能的研究方向。