Spline Approximation Method for Solving Self-Adjoint Singular Perturbation Problems on Non-Uniform Grids

A numerical method based on cubic spline with adaptive grid is given for the self-adjoint singularly perturbed two point boundary value problems. The scheme derived in this method is second order accurate. Numerical examples are given to support the predicted theory.     

2‐D transmitral flows simulation by means of the immersed boundary method on unstructured grids

Interaction between computational fluid dynamics and clinical researches recently allowed a deeper understanding of the physiology of complex phenomena involving cardio‐vascular mechanisms. The aim of this paper is to develop a simplified numerical model based on the Immersed Boundary Method and to perform numerical simulations in order to study the cardiac diastolic phase during which the left ventricle is filled with blood flowing from the atrium throughout the mitral valve. As one of the diagnostic problems to be faced by clinicians is the lack of a univocal definition of the diastolic performance from the velocity measurements obtained by Eco–Doppler techniques, numerical simulations are supposed to provide an insight both into the physics of the diastole and into the interpretation of experimental data. An innovative application of the Immersed Boundary Method on unstructured grids is presented, fulfilling accuracy requirements related to the development of a thin boundary layer along the moving immersed boundary. It appears that this coupling between unstructured meshes and the Immersed Boundary Method is a promising technique when a wide range of spatial scales is involved together with a moving boundary. Numerical simulations are performed in a range of physiological parameters and a qualitative comparison with experimental data is presented, in order to demonstrate that, despite the simplified model, the main physiological characteristics of the diastole are well represented. Copyright © 2002 John Wiley & Sons, Ltd.     

离心压缩机直纹面叶轮的网格生成方法

采用三次非均匀B样条技术,对直纹面叶片的离心压缩机叶轮通道的网格生成方法进行了研究。详细介绍了相关的B样条理论及采用人工编程生成网格的方法和步骤,在此基础上对NASALSCC直纹面叶轮叶片通道实现了三维网格生成,并对网格的正交性进行了量化评估。     

Local defect correction with different grid types

For a Poisson problem with a solution having large gradients in (nearly) circular subregions a local defect correction method is considered. The problem on the global domain is discretized on a cartesian grid, whereas the restriction of the problem to a circular subdomain is discretized on a polar grid. The two discretizations are then combined in an iterative way. We show that LDC can be viewed as an iterative method for the Poisson equation on a single composite cartesian‐polar grid. The efficiency of methods is illustrated by numerical examples. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 454–468, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/num.10018     

交通事故统计监控系统的设计

本文针对全国交通事故平均数呈现上升趋势等新情况 ,给出交通事故统计分析与监控管理的数学模型 ,所用的统计方法是面向计算机、适应于计算机并应用计算机进行动态监控的数学方法。为交通管理提供科学的决策 ,使交通事故管理向科学化与现代化迈进     

指数扩展格网络方法：模拟球、柱和旋转圆盘电极体系电化学问题的有效方法

An exponentially expanded space grid technique has been employed in the network simulation of chronoamperometric and voltammetric problems in spherical, cylindrical and rotating-disk electrode systems, leading to an effective simulation strategy for electrochemical problems: exponentially expanded grid network approach (EEGNA). The success of this method is largely due to the improved ability in processing the boundary singularities existing for non-planar diffusions and the enhanced simulation speed and accuracy in contrast to the uniform or quasi-uniform grid network approach.     

Use of Divided Differences and B Splines for Constructing Fast Discrete Transforms of Wavelet Type on Nonuniform Grids

In this paper, we construct fast discrete transforms of wavelet type with an arbitrary number of zero moments for nonuniform grids. We obtain explicit formulas for the parameters defining the wavelet transform.__________Translated from Matematicheskie Zametki, vol. 77, no. 5, 2005, pp. 743–752.Original Russian Text Copyright ©2005 by I. V. Oseledets.     

Internal wave computations using the ghost fluid method on unstructured grids

Two‐layer incompressible flows are analysed using the ghost fluid method on unstructured grids. Discontinuities in dynamic pressure along interfaces are captured in one cell without oscillations. Because of data reconstructions based on gradients, the ghost fluid method can be adopted without additional storages for the ghost nodes at the expense of modification in gradient calculations due to the discontinuity. The code is validated through comparisons with experimental and other numerical results. Good agreements are achieved for internal waves generated by a body moving at transcritical speeds including a case where upstream solitary internal waves propagate. The developed code is applied to analyse internal waves generated by a NACA0012 section moving near interfaces. Variations of the lift acting on the body and configurations of the interfaces are compared for various distances between the wing and the interface. The effects of the interface are compared with the effects of a solid wall. Copyright © 2004 John Wiley & Sons, Ltd.     

两介质段瞬变流的修正特征线法

本文针对变波速可压缩两介质段非定常流的数值模拟,提出了修正特征线法。为使计算网格保持矩形,将一个大于1的修正因子α引入动量方程,从而在一定的范围内对特征线斜率进行调整,并据此确定时间和空间步长。其中因不满足稳定性条件而造成的误差由修正因子对动量方程进行修正。这种方法适用于一般瞬变流和振荡流。为解决介质界面连续移动的问题,本文提出了可自动调节空间步长的浮动网格,这使计算单元介质得以保持单一。通过在压力项中加入人工粘性改善了计算的稳定性。文章最后给出了计算实例。     

Comments on algorithms for grid interfaces in simulating Euler flows

Some results concerning the algorithms for grid interfaces, which are crucial in simulating flows by zonal methods, are presented in this paper. It is indicated that the commonly used conservative interface scheme can ensure the discrete entropy condition, but it may be inconsistent and would bring a nonoverlapping solution on overlapping grids. A nonconservative interface matching obtained by interpolation can be monotonicity preserving, and it leads large conservation error when discontinuities are close to the interfaces. Methods for improvement of interface algorithms are also proposed.