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构建对流扩散方程不振荡有限体积格式的高算法

发表时间:2011-02-15  浏览量:1335  下载量:436
全部作者: 杨满叶,舒适,李明军
作者单位: 湘潭大学数学与计算科学学院;中国科学院力学研究所
摘 要: 提出一些构建方法,如熟知的人工粘性Jameson格式、通量限制器和增加模板点ENO/WENO格式等。数值摄动算法通过对常见格式的摄动重构,把下游不影响上游的对流运动规律、高阶流体力学线性关系与之耦合,可以构建成高阶不振荡迎风和中心格式有限差分格式和有限体积格式,简称高迎风格式(Gao’s upwind schemes,GUS)和高中心格式(Gao’s center schemes,GCS),如三结点的GUS和GCS、五结点GUS和高-QUICK格式。讨论了这一构建不振荡格式有限体积的新方法,通过5个算例的数值计算证实了新格式的优良性质,说明不振荡高格式具有很大的工程应用前景。
关 键 词: 计算流体力学;高中心有限体积格式;二阶中心格式;数值摄动高精度重构;不振荡格式
Title: Gao’s algorithm for constructing computational fluid dynamics non-oscillatory finite volume schemes
Author: YANG Manye, SHU Shi, LI Mingjun
Organization: School of Mathematics and Computational Science, Xiangtan University; Institute of Mechanics, Chinese Academy of Sciences
Abstract: Some constructing methods were put forward including artificial viscosity such as Jameson scheme, flux-limiter, increasing template points such as ENO/WENO and so on. Gao’s algorithm can construct analytically cmputational fluid dynamics (CFD) non-oscillatory schemes by coupling simple mathematical schemes for the convective-diffusion equation with both the higher-order fluid mechanics relations and the convective motion laws of upstream state being not affected by downstream information. Some absolute positive upwind and central finite volume schemes are evaluated. These schemes were called Gao’s upwind schemes (GUS) and Gao’s central scheme (GCS) for convenience. Some three-nodes GUS and GCS, five-nodes GUS and G-QUICK are listed. These schemes absolutely have very huge application prospect. Excellent properties of Gao schemes for the convective-diffusion equation are proved by analysis and five numerical test in this paper.
Key words: computational fluid dynamics; Gao’s center finite volume scheme; second-central scheme; high-presicion numerical perturbation algorithm; non-oscillatory scheme
发表期数: 2011年2月第3期
引用格式: 杨满叶,舒适,李明军. 构建对流扩散方程不振荡有限体积格式的高算法[J]. 中国科技论文在线精品论文,2011,4(3):221-227.
 
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