间断数值摄动算法及NS方程高精度中心有限体积格式与应用

项目名称： 间断数值摄动算法及NS方程高精度中心有限体积格式与应用

项目编号： No.11272324

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 高智

作者单位： 中国科学院力学研究所

项目金额： 80万元

中文摘要： 近几十年计算流体力学（CFD）飞速发展，它在航天航空等领域的流动模型中应用越来越广泛、作用越来越大，它的一个关键是算法，发展趋势和热点是构造能适应非结构等复杂网格的高性能算法，并被软件所使用。申请人提出的数值摄动算法是原创算法。NS方程的迎风摄动格式计算复杂流动具有很好的表现。在刚结题的基金面上项目研究中，我们又提出间断摄动、构建了对流扩散方程的间断摄动中心有限体积（FV）格式和差分（FD）格式，这些格式精度高绝对稳定，简单，不用限制器不用人工粘性，且得到分析和数值证实。本项目开展NS方程间断摄动研究，间断摄动AUSM类格式建成4类NS方程高精度不振荡中心FV格式，并对它们补充摄动反应项，建成4类反应流NS高精度不振荡中心FV格式；构建压力SIMPLE计算的两类NS高精度不振荡中心FV格式；通过复杂流动计算和与其它高精度格式的比较检验，使这十类格式成为NS高性能实用格式。

中文关键词： 计算流体力学；数值摄动算法；摄动加权基本无振荡格式；源项刚性问题；干扰剪切扰动流稳定性理论

英文摘要： Computational fluid dynamics (CFD) has been developing rapidly in recent half century. CFD has been applying more and more universally to numerical simulation of fluid flows in the fields of aerospace and aeronautics and so on and its effects become more and more great. A key of CFD is algorithm (or scheme) whose developing trend and studying focus are to construct higher performance schemes which are suitable to unstructured and complewx grids. These new schemes ought to be used in CFD software. The numerical pertubation algorithm presented by the author is an original innovative algorithm. The numerical results given by the upwind perturbation NS schemes computing complex flows are very good. A discontinuous numerical perturbation algorithm was presented by the author in studying NNSF project just finished. Some central finite volume (FV) schemes and central finite difference (FD) schemes for convective diffusion equation were constructed by discontinuous perturbation, theses schemes have excellent properties: higher-order accurate, non-oscillatory, simplicity, calculated amount less, no use limiter, no use artificial viscosity, the central FV schemes use the least cell and aresuitable to unstructured and complex grids. The excellent properties of thses schemes above stated are proved by analyses and calculati

英文关键词： computational fluid dynamics；numerical perturbation algorithm；perturbational WENO scheme；numerical stiff problem；interacting shear flow stability theory