| 用物理黏性构建高阶不振荡对流扩散差分格式 | |
| Alternative Title | HIGHER-ORDER ACCURATE,NON-OSCILLATORY,THREE-NODES CENTRAL DIFFERENCE SCHEME FOR THE CONVECTIVE-DIFFUSION EQUATION CONSTRUCTED BY USING PHYSICAL VISCOSITY |
高智
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| Source Publication | 力学学报
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| 2012-05-18 | |
| Volume | 44Issue:3Pages:505-512 |
| ISSN | 0459-1879 |
| Abstract | 利用数值摄动算法,通过扩散格式数值摄动重构把对流扩散方程的2阶中心差分格式(2-CDS)重构为高精度高分辨率格式,解析分析和模型方程计算证实了新格式的高精度不振荡性质.新格式是把物理黏性使流动光滑化的扩散运动规律引入2-CDS中的结果.该法显然与构建高级离散格式的常见方法不同.证实:数值摄动重构中引入扩散运动规律的结果格式与引入对流运动规律(下游不影响上游的规律)的结果格式一致,说明对离散方程的数值摄动运算,在维持原格式结构形式不动的条件下,不仅能提高格式精度和稳健性,且可揭示对流离散运动规律与扩散离散运动规律之间的内在关联;同时证实,文中提出和使用的上、下游分裂方法是构建高精度不振荡离散格式的一个有效方法. |
| Other Abstract | Several higher-order accurate, non-oscillatory, three-nodes central difference schemes for the convective-diffusion equation are given by perturbationally reconstructing the diffusion scheme in the second-order accurate central difference scheme (2-CDS). Excellent properties of higher-order accurate and high resolution of the present new schemes (diffusion perturbation schemes, DPS) are verified by theoertical analyses and three numerical tests which include one-dimensional linear and non-linear and two-dimensional convective-diffusion equations. In all numerical tests, the 2-CDS oscillates and diverges on coarse grids, while part of DPS do not oscillates and can capture discontinuities with high resolution. The mean square root L2 errors of all DPS are greatly less than those of 2-CDS in all numerical tests. The DPS are the results of introducing diffusion-motion law (i. e. physical viscosity smoothing out space-distribution of diffusion quantities) into 2-CDS. The present method is obviously different from the well-known those of constructing high-order accurate and high resolution schemes. In addition, we prove that DPS are completely consistent with those schemes of introducing convection-motion law (i. e. law of that the downstream does not affect the upstream) into 2-CDS, to show that the perturbational operation to 2-CDS not only raises the scheme's accurate and stability but also reveals intrinsic relation between the convective discrete scheme and diffusion discrete scheme, and that the upstream-downstream splitting is a very useful method for reconstructing high-order accurate, high resolution CFD scheme without artificial viscosity or limiter. |
| Keyword | 计算流体力学 数值摄动算法 高精度不振荡差分格式 对流扩散方程 |
| Subject Area | 计算流体力学 |
| URL | 查看原文 |
| Indexed By | CSCD ; EI |
| Language | 中文 |
| Funding Organization | 国家自然科学基金资助项目(10872204) |
| CSCD ID | CSCD:4544804 |
| Classification | 二类 |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://dspace.imech.ac.cn/handle/311007/46524 |
| Collection | 高温气体动力学国家重点实验室 |
| Corresponding Author | 高智 |
| Recommended Citation GB/T 7714 | 高智. 用物理黏性构建高阶不振荡对流扩散差分格式[J]. 力学学报,2012,44,3,:505-512. |
| APA | 高智.(2012).用物理黏性构建高阶不振荡对流扩散差分格式.力学学报,44(3),505-512. |
| MLA | 高智."用物理黏性构建高阶不振荡对流扩散差分格式".力学学报 44.3(2012):505-512. |
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