KT格式数值求解几类典型流体力学问题

发布时间：2018-05-10 19:08

本文选题：KT格式 + 中心格式　；参考：《沈阳师范大学》2017年硕士论文

【摘要】：KT格式是Kurganov和Tadmor于2000年提出的一种用来求解双曲守恒律的高精度中心格式。该格式利用波在当地传播的最大速度来估计黎曼扇的宽度,从而将计算区域分为光滑区域和非光滑区域,并对两部分分别进行积分求解。KT格式除了具有中心格式所具有的无需求解黎曼求解器,算法简单的优点以外,该格式还具有数值耗散小,稳定性高,捕捉激波能力强等特点。本文利用KT格式分别求解一维、二维激波管问题,并利用该格式计算双马赫反射问题,通过将计算结果与其他几种经典格式进行比较,发现KT格式在间断处展现出更高的精度。本文结果很好地支持了KT格式理论。论文分为五个部分:第一章介绍了本文所讨论的主要内容、国内外研究现状;第二章介绍了激波管问题、双马赫反射问题以及问题所用控制方程;第三章详细介绍了KT格式、以及时间离散所用的Runge-Kutta法和计算的条件;第四章分别对一维激波管问题、二维激波管问题和双马赫反射问题进行结果分析,对比不同格式的性能;最后得到文章结论,对未来的研究方向进行了展望。
[Abstract]:KT scheme is a high-precision center scheme proposed by Kurganov and Tadmor in 2000 to solve hyperbolic conservation law. In this scheme, the width of Riemann fan is estimated by using the maximum velocity of local wave propagation, and the calculated region is divided into smooth region and non-smooth region. In addition to the advantages of the central scheme without Riemannian solver and simple algorithm, the KT scheme has the advantages of small numerical dissipation, high stability and strong ability to capture shock waves. In this paper, the one-dimensional and two-dimensional shock tube problems are solved by using KT scheme, and the double Mach reflection problem is calculated by using this scheme. By comparing the results with other classical schemes, it is found that the KT scheme exhibits a higher accuracy at the discontinuity. The results of this paper support the theory of KT scheme well. The thesis is divided into five parts: the first chapter introduces the main contents discussed in this paper, the domestic and foreign research status, the second chapter introduces the shock tube problem, the double Mach reflection problem and the governing equations used in the problem; the third chapter introduces the KT scheme in detail. In chapter 4, the results of one-dimensional shock tube problem, two-dimensional shock tube problem and double Mach reflection problem are analyzed, and the performances of different schemes are compared. The future research direction is prospected.
【学位授予单位】：沈阳师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O35;O241.8

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