MPI平台下二维欧拉方程数值解法

【作者】 韦祥文；

【导师】 徐敏；

【作者基本信息】 西北工业大学 ， 飞行器设计， 2003， 硕士

【摘要】 我们知道，由于流场的复杂性，要有足够多的网格点才能分辨出流场的细微结构。另外，在非定常流的模拟中，需要获得流动随时间的变化过程，这使得计算工作量变得十分巨大。为了使冗长的求解过程达到工程上可以接受的程度，以利于实际应用，必须缩短计算时间提高计算效率。目前解决问题的主要途径有两条：一是改善数值方法，利用各种收敛技术来减少计算时间；二是利用并行环境，实现软件的多机并行计算，达到大幅度降低计算时间的目的，使得某些巨型计算成为可能。 本论文采用欧拉方程作为控制方程，利用中心有限体积法进行空间离散，得到对时间变量的常微分方程组，采用龙格库塔多步法进行时间积分，加入人工粘性以消除激波和驻点附近的压力振荡等方法来对NACA0012翼型的实际流动进行并行数值模拟。 本论文的工作主要包括以下三个方面： (1) 给出单机完成流场计算的例子，作为与并行计算比较的基础。 (2) 利用以太网来连接一组微机，以Linux操作系统和消息传递接口(Message Passing Interface, MPI)为并行程序开发环境，建立了集群式的并行计算系统。 (3) 采用MPI并行编程方法实现流场数值计算的并行化，并对影响并行效率的负载分配、通信等因素进行了研究。更多还原

【Abstract】 As we know, much more grid points are required in order to differentiate the structure of flow field, which is extremely complex. In addition, unsteady flow simulation needs to gain flow movement along time. As a result, the computing task of the numerical simulation is very great. In order to make the long computing can be expediently applied to engineering, the computing time have to be decreased and the efficiency must be increased. There are two main ways that will be effective to solve the question currently: one is to improving numerical algorithm by all kinds of skills to accelerate convergence; the other is to introducing parallel computing.In order to work out the numerical simulation of flow in NACA0012, Euler equations are selected as the control equations of the flow field in this paper. The main numerical method of this code is coming from scheme (Jameson, Schimit and Turkel): using cell-centered finite volume method as spatial discretization tools, and a system of ordinary differential equations for time variable is obtained, which is solved by utilizing five-step Runge-Kutta scheme as time marching method , introducing artificial dissipation to damp high frequency oscillations near the shock and stagnation point.The thesis is focused on the following aspects:1 .As the base of comparison with parallel computing, an example which is completed on single processor is given.2.Cluster of workstation (COW) has been established as a parallel computing platform.3.A parallel computing program of two-dimension flow numerical calculation has been completed. Some important techniques such as communication among nodes and load balancing are analyzed.更多还原