可压不可压流动新型统一算法研究

项目名称： 可压不可压流动新型统一算法研究

项目编号： No.50806037

项目类型： 青年科学基金项目

立项/批准年度： 2009

项目学科： 轻工业、手工业

项目作者： 李雪松

作者单位： 清华大学

项目金额： 21万元

中文摘要： 本研究中，首先提出了新型方法全速度Roe格式，克服了传统统一算法需要全局截断的弱点，并且明确指出预处理收敛加速能力主要来自于预处理矩阵本身，而与格式耗散构造基本无关。进而推导并讨论了将动量插值方法具体实现到时间推进框架下的统一算法形式，阐明了动量插值方法与传统处理方法的区别与联系。尤其重要的是，通过这一研究认识到激波捕获格式具有内在的类似于动量插值的压力锯齿波抑制机制。在以上研究基础上，通过对五种不同的Roe型格式进行深入的对比与研究，揭示了这些方法的内在规律，获得对这些方法的统一认识。分别从精度、压力锯齿波、全局截断问题这三个方面，揭示了Roe型统一算法具有普遍意义的核心机制。随后将核心机制应用到其它经典激波捕获格式，如HLL与预处理HLL格式中，解释了预处理HLL格式特殊的困难，并提出新方法解决了这一困难。更重要的是，这一研究进一步显示了核心机制的普适性与理论价值。研究表明，这一核心机制不但可以统一解释已有的各种方法成败得失及其原因，而且可以指导构造更多更好的新方法，可以看作是"方法的方法"。已在国际著名期刊发表SCI论文2篇，EI论文2篇，国内会议论文3篇，另有两篇论文在投。

中文关键词： 预处理；Roe格式；HLL格式；压力锯齿；全局截断

英文摘要： This research firstly proposed a new method, All-Speed Roe scheme, to ovecome the global cut-off limitation of the traditonal preconditioning method. It also pointed out that the convergence acceleration of preconditioning is mainly due to the preconditioner and is independent of the numerical dissipation to a great extent. Further, the momentum interpolation method is deduced under the frame of the time-marching algorithm. Importantly, it realized that the shock-capture scheme has an inherent coarse version of the time-marching momentum interpolation method to suppress the checkerboard pressure because of the similar mechanism of introducing pressure derivatives into the interface velocity and its lower order numerical errors. Base on this understanding and the analysis of the five Roe-type schemes, three mechanisms was discovered from the angles of the accuracy, checkerboard pressure, and the global cut-off problems, respectively. Finally, the mechanisms were also applied to the classical and preconditioned HLL schemes. It explained the peculiar limitation of the preconditionded HLL scheme and then guided a new modified HLL scheme to overcome the difficulty. More Importantly, this study showed the generality and theoretical value of the three mechanisms. Thus, the mechanisms can be regarded as the "method's method", because it can explain the advantage and disadvantage of the developed schemes, and can help us proposing better schemes.

英文关键词： preconditioning; Roe scheme; HLL scheme; checkerboard pressure; global cutoff