High-Resolution Finite Compact Difference Schemes for Hyperbolic Conservation Laws

A finite compact (FC) difference scheme requiring only bi-diagonal matrix inversion is proposed by using the known high-resolution flux. Introducing TVD or ENO limiters in the numerical flux, several high-resolution FC-schemes of hyperbolic conservation law are developed, including the FC-TVD, third-order FC-ENO and fifth-order FC-ENO schemes. Boundary conditions formulated need only one unknown variable for third-order FC-ENO scheme and two unknown variables for fifth-order FC-ENO scheme. Numerical test results of the proposed FC-scheme were compared with traditional TVD, ENO and WENO schemes to demonstrate its high-order accuracy and high-resolution.

A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations.

The effects of complex boundary conditions on flows are represented by a volume force in the immersed boundary methods. The problem with this representation is that the volume force exhibits non-physical oscillations in moving boundary simulations. A smoothing technique for discrete delta functions has been developed in this paper to suppress the non-physical oscillations in the volume forces. We have found that the non-physical oscillations are mainly due to the fact that the derivatives of the regular discrete delta functions do not satisfy certain moment conditions. It has been shown that the smoothed discrete delta functions constructed in this paper have one-order higher derivative than the regular ones. Moreover, not only the smoothed discrete delta functions satisfy the first two discrete moment conditions, but also their derivatives satisfy one-order higher moment condition than the regular ones. The smoothed discrete delta functions are tested by three test cases: a one-dimensional heat equation with a moving singular force, a two-dimensional flow past an oscillating cylinder, and the vortex-induced vibration of a cylinder. The numerical examples in these cases demonstrate that the smoothed discrete delta functions can effectively suppress the non-physical oscillations in the volume forces and improve the accuracy of the immersed boundary method with direct forcing in moving boundary simulations.

Smoothing effect in the broadband laser through a dispersive wedge

The propagation expression of a broadband laser passing through a dispersive wedge is derived on the basis of the Huygens-Fresnel diffraction integral, Smoothing effects caused by the phase perturbation of the dispersive wedge on the intensity profiles are investigated in detail. The phase perturbation of the dispersive wedge induces a relative transverse position shift between the diffraction patterns of different frequency components. The relative transverse position shift is of great benefit to the fill of the intensity peaks of some patterns in the valleys of others when these patterns are overlapped and thus the smoothing effect is achieved. (c) 2006 Elsevier B.V. All rights reserved.

Beam smoothing by lens array with spectral dispersion

A scheme of combining technology of lens array (LA) and smoothing by spectral dispersion (SSD) is introduced to improve the irradiation uniformity in laser fusion based on the earlier works on LA. The feasibility of the scheme is also analyzed by numerical simulation. It shows that a focal pattern with flat-top and sharp-edge profile could be obtained, and the irradiation nonuniformity can fall down from 14% with only LA to 3% with both SSD and LA. And this smoothing scheme is depended less on the incidence comparing to other smoothing methods. The preliminary experiment has demonstrated its effectiveness. (c) 2006 Elsevier B.V. All rights reserved.

Smoothing the side lobes of a focused pattern by spectral dispersion in the broadband laser

Starting from the Huygens-Fresnel diffraction integral, the propagation equations of a broadband laser passing through a dispersive lens and a dispersive wedge are derived. Smoothing effect on the side lobes of the focused pattern is achieved as the broadband laser passes through the lens because of the spectral dispersion of the lens. By inserting a dispersive wedge behind the lens, better smoothing effect is realized because a relative position shift between focused patterns of different frequency components is generated due to the spectral dispersion of the wedge. Smoothing effect on the side lobe is obtained even with small bandwidth of the broadband laser as the wedge is used. (c) 2006 Elsevier GmbH. All rights reserved.

Smoothing LDA Model for Text Categorization

Abstract. Latent Dirichlet Allocation (LDA) is a document level language model. In general, LDA employ the symmetry Dirichlet distribution as prior of the topic-words’ distributions to implement model smoothing. In this paper, we propose a data-driven smoothing strategy in which probability mass is allocated from smoothing-data to latent variables by the intrinsic inference procedure of LDA. In such a way, the arbitrariness of choosing latent variables'priors for the multi-level graphical model is overcome. Following this data-driven strategy,two concrete methods, Laplacian smoothing and Jelinek-Mercer smoothing, are employed to LDA model. Evaluations on different text categorization collections show data-driven smoothing can significantly improve the performance in balanced and unbalanced corpora.

smoothing document language model with local word graph

ACM SIGIR; ACM SIGWEB

LEAST-SQUARES POLYNOMIAL SMOOTHING FOR INDUCTIVELY COUPLED PLASMA ATOMIC EMISSION-SPECTRA

The use of least-squres polynomial smoothing in ICP-AES is discussed and a method of points insertion into spectral scanning intervals is proposed in the present paper. Optimal FWHM/SR ratio can be obtained, and distortion of smoothed spectra can be avoided by use of the recommended method.

Simulation of Free-Surface Flow in a Tank Using the Navier-Stokes Model and Unstructured Finite Volume Method

Modelling free-surface flow has very important applications in many engineering areas such as oil transportation and offshore structures. Current research focuses on the modelling of free surface flow in a tank by solving the Navier-Stokes equation. An unstructured finite volume method is used to discretize the governing equations. The free surface is tracked by dynamically adapting the mesh and making it always surface conforming. A mesh-smoothing scheme based on the spring analogy is also implemented to ensure mesh quality throughout the computaiton. Studies are performed on the sloshing response of a liquid in an elastic container subjected to various excitation frequencies. Further investigations are also carried out on the critical frequency that leads to large deformation of the tank walls. Another numerical simulation involves the free-surface flow past as submerged obstacle placed in the tank to show the flow separation and vortices. All these cases demonstrate the capability of this numerical method in modelling complicated practical problems.

双曲守恒型方程的二阶摄动有限差分格式

对双曲守恒型方程，将其一阶迎风格式空间差商的常系数摄动展开为时间步长和空间步长的幂级数，通过确定幂级数系数而获得二阶精度的摄动有限差分（PFD）格式。进而从双曲守恒型方程的通量分裂型一阶迎风格式出发，通过娄似的摄动展开方法，获得空间精度为二阶的通量分裂形式的摄动有限差分（FPFD）格式。这两类格式保留了一阶守恒迎风格式的简洁结构形式，使用三节点即可达到二阶精度，又避免了三点二阶格式的非物理数值振荡。并将这两类格式推广应用到双曲守恒型方程组，最后通过模型方程和一维激波管流动的数值算例验证了格式的高精度、高分辨率性质。

An improvement and proof of OGY method

OGY method is the most important method of controlling chaos. It stabilizes a hyperbolic periodic orbit by making small perturbations for a system parameter. This paper improves the method of choosing parameter, and gives a mathematics proof of it.

Direct Numerical Simulation Of Hypersonic Boundary-Layer Transition Over A Blunt Cone

Direct numerical simulation of transition How over a blunt cone with a freestream Mach number of 6, Reynolds number of 10,000 based on the nose radius, and a 1-deg angle of attack is performed by using a seventh-order weighted essentially nonoscillatory scheme for the convection terms of the Navier-Stokes equations, together with an eighth-order central finite difference scheme for the viscous terms. The wall blow-and-suction perturbations, including random perturbation and multifrequency perturbation, are used to trigger the transition. The maximum amplitude of the wall-normal velocity disturbance is set to 1% of the freestream velocity. The obtained transition locations on the cone surface agree well with each other far both cases. Transition onset is located at about 500 times the nose radius in the leeward section and 750 times the nose radius in the windward section. The frequency spectrum of velocity and pressure fluctuations at different streamwise locations are analyzed and compared with the linear stability theory. The second-mode disturbance wave is deemed to be the dominating disturbance because the growth rate of the second mode is much higher than the first mode. The reason why transition in the leeward section occurs earlier than that in the windward section is analyzed. It is not because of higher local growth rate of disturbance waves in the leeward section, but because the growth start location of the dominating second-mode wave in the leeward section is much earlier than that in the windward section.

A Multimoment Finite-Volume Shallow-Water Model On The Yin-Yang Overset Spherical Grid

A numerical model for shallow-water equations has been built and tested on the Yin-Yang overset spherical grid. A high-order multimoment finite-volume method is used for the spatial discretization in which two kinds of so-called moments of the physical field [i.e., the volume integrated average ( VIA) and the point value (PV)] are treated as the model variables and updated separately in time. In the present model, the PV is computed by the semi-implicit semi-Lagrangian formulation, whereas the VIA is predicted in time via a flux-based finite-volume method and is numerically conserved on each component grid. The concept of including an extra moment (i.e., the volume-integrated value) to enforce the numerical conservativeness provides a general methodology and applies to the existing semi-implicit semi-Lagrangian formulations. Based on both VIA and PV, the high-order interpolation reconstruction can only be done over a single grid cell, which then minimizes the overlapping zone between the Yin and Yang components and effectively reduces the numerical errors introduced in the interpolation required to communicate the data between the two components. The present model completely gets around the singularity and grid convergence in the polar regions of the conventional longitude-latitude grid. Being an issue demanding further investigation, the high-order interpolation across the overlapping region of the Yin-Yang grid in the current model does not rigorously guarantee the numerical conservativeness. Nevertheless, these numerical tests show that the global conservation error in the present model is negligibly small. The model has competitive accuracy and efficiency.

Analysis and application of ellipticity of stability equations on fluid mechanics

By using characteristic analysis of the linear and nonlinear parabolic stability equations (PSE), PSE of primitive disturbance variables are proved to be parabolic intotal. By using sub-characteristic analysis of PSE, the linear PSE are proved to be elliptical and hyperbolic-parabolic for velocity U, in subsonic and supersonic, respectively; the nonlinear PSE are proved to be elliptical and hyperbolic-parabolic for relocity U + u in subsonic and supersonic, respectively. The methods are gained that the remained ellipticity is removed from the PSE by characteristic and sub-characteristic theories, the results for the linear PSE are consistent with the known results, and the influence of the Mach number is also given out. At the same time, the methods of removing the remained ellipticity are further obtained from the nonlinear PSE.