用物理黏性构建高阶不振荡对流扩散差分格式

高智

doi:10.6052/0459-1879-2012-3-20120306

用物理黏性构建高阶不振荡对流扩散差分格式

高智

中国科学院力学研究所高温气体动力学国家重点实验室, 北京 100190

基金项目: 国家自然科学基金资助项目(10872204).

详细信息

中图分类号: O357
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出版历程
- 收稿日期: 2011-06-06
- 修回日期: 2011-11-06
- 刊出日期: 2012-05-17

HIGHER-ORDER ACCURATE, NON-OSCILLATORY, THREE-NODES CENTRAL DIFFERENCE SCHEME FOR THE CONVECTIVE-DIFFUSION EQUATION CONSTRUCTED BY USING PHYSICAL VISCOSITY

Gao Zhi

State Key Laboratory of High Temperature Gasdynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China

Funds: The project was supported by the National Natural Science Foundation of China (10872204)

摘要

摘要: 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.
- 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
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.
- computational fluid dynamics /
- numerical perturbation algorithm /
- high-order accurate and non-oscillatory scheme /
- convection-diffusion equation

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参考文献(15)

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