Adaptive mesh refinement computation of acoustic radiation from an engine intake

A block-structured adaptive mesh refinement (AMR) method was applied to the computational problem of acoustic radiation from an aeroengine intake. The aim is to improve the computational and storage efficiency in aeroengine noise prediction through reduction of computational cells. A parallel implementation of the adaptive mesh refinement algorithm was achieved using message passing interface. It combined a range of 2nd- and 4th-order spatial stencils, a 4th-order low-dissipation and low-dispersion Runge–Kutta scheme for time integration and several different interpolation methods. Both the parallel AMR algorithms and numerical issues were introduced briefly in this work. To solve the problem of acoustic radiation from an aeroengine intake, the code was extended to support body-fitted grid structures. The problem of acoustic radiation was solved with linearised Euler equations. The AMR results were compared with the previous results computed on a uniformly fine mesh to demonstrate the accuracy and the efficiency of the current AMR strategy. As the computational load of the whole adaptively refined mesh has to be balanced between nodes on-line, the parallel performance of the existing code deteriorates along with the increase of processors due to the expensive inter-nodes memory communication costs. The potential solution was suggested in the end.     

高等数学中一类证明题的解题方法

在专升本高等数学的考试中,证明题占有举足轻重的地位。总结在考试中常见的两种类型证明问题,并给出一种构造辅助函数的方法,最后通过例题检验该方法的有效性。     

Performance optimization of grooved slippers for aero hydraulic pumps

A computational fluid dynamics(CFD) simulation method based on 3-D Navier–Stokes equation and Arbitrary Lagrangian–Eulerian(ALE) method is presented to analyze the grooved slipper performance of piston pump.The moving domain of grooved slipper is transformed into a fixed reference domain by the ALE method,which makes it convenient to take the effects of rotate speed,body force,temperature,and oil viscosity into account.A geometric model to express the complex structure,which covers the orifice of piston and slipper,vented groove and the oil film,is constructed.Corresponding to different oil film thicknesses calculated in light of hydrostatic equilibrium theory and boundary conditions,a set of simulations is conducted in COMSOL to analyze the pump characteristics and effects of geometry(groove width and radius,orifice size) on these characteristics.Furthermore,the mechanics and hydraulics analyses are employed to validate the CFD model,and there is an excellent agreement between simulation and analytical results.The simulation results show that the sealing land radius,orifice size and groove width all dramatically affect the slipper behavior,and an optimum tradeoff among these factors is conducive to optimizing the pump design.     

四色定理论证

用离散数学之图论证明"四色猜想",巧妙而深层次地应用数学归纳法和换色法,解决了肯泊(A.Kempe)百多年前提出"不可避免构形集"中的一个地域有五个邻域的情况的所谓"可约性"问题,同时指出了1890年希伍德(P.Heawood)举出的25阶反例(当时,他以此说明"四色猜想"不成立,而"五色定理"成立)与本文中的一种可换色(即"可约性")的典型实例类同,进而简捷而理想地证明了"四色猜想"是成立的,使"四色定理"得到科学的论证。     

航空公司实行多级票价的经济数学模型

首先利用经济学理论对航空公司实施多级票价体系的定价策略进行分析,得出多级票价体系的实施可以使航空公司和旅客实现共赢的结论。在此基础上,通过构建经济数学模型来指导航空公司如何制定多级票价体系。最后指出了航空公司制定多级票价体系的关键问题和应对策略。     

浅谈数学建模及竞赛辅导

本论述了数学模型的一般概念，讨论了数学模型的分类及数学模型的步骤和方法，通过两个建模实例，结合作辅导建模竞赛的经验，研究了建模竞赛的组织与训练问题。     

Navier—Stokes（NS）方程组差分计算中的物理和网格尺度效应及NS方程组的简化

对于高Re数流动计算，在通常二阶精度NS差分格式和网格数条件下，存在某些粘性项落入修正微分方程截断误差项的问题。这类NS方程组计算实际是计算某种简化NS方程组，而且重复计算误差物理粘性项既浪费机时和内存，误差积累又会对数值解产生不可预测的影响，避免外述缺陷的办法一个提高NS差分格式的精度，另一个是丢掉可能落入截断误差项的物理粘性项，把NS方程组简化为广义NS方程组，广义NS计算避免了误差物理粘性项误差积累对数值解的不可知影响，又可节省内存和机时，对高Re数流体工程计算很有好处。利用广义NS方程组计算超声速绕前向和后向台阶流动的结果表明：广义NS方程组与NS方程组的数值结果很好相符符。     

航空直流起动发电机起动过程分析

航空直流起动发电机驱动飞机发动机起动要经历多次换路,分析了每次换路的物理过程,建立了起动过程的动态模型和状态方程。利用该数学模型计算了航空直流起动发电机的起动过程,所计算的物理量包括电流、转速、转矩等。按计算结果画出了动态曲线,使用软件MATLAB编程实现计算。     

网格分区构筑中区域边界的隐式处理方法

介绍一种网格分区构筑中区域边界的隐式处理方法──ADMZI法。该方法具有简单实用、数据结构灵活等特点,特别适合于区域边界难以确定的情况。将该方法应用于多级火箭级间分离时的流场物理域网格构筑,结果证明是成功的。     

模糊数学在飞机飞控系统故障诊断的应用

基于A320系列客机飞控系统,分析了飞机系统故障诊断的特点,建立了针对飞控系统的故障诊断系统,并且设计了数据库服务。应用模糊数学的方法建立了专家系统,使飞机故障诊断系统更具有实用性和科学性,为飞机故障诊断提供一种比较有效的方法。