摘要
利用高智提出的数值摄动算法,把对流扩散方程的常用QUICK格式(黏性和对流项分别用二阶中心和QUICK格式离散)进行了高精度重构,包括利用离散单元内所有结点的全域重构和分别利用离散单元内上下游结点的上下游重构,得到两类新的更高阶精度的数值摄动重构格式,称为高的QUICK格式(G-QUICK格式).G-QUICK格式与QUICK格式相比简单性相当,但精度更高;全域重构G-QUICK格式和QUICK格式均为条件稳定,上下游重构得到一些绝对稳定的G-QUICK格式.解析分析和数值算例均证实了G-QUICK格式的优良性能,上下游重构的G-QUICK格式为在对流扩散方程的QUICK格式中避免使用人工黏性提供了新途径.
In this paper some higher-order accurate reconstruction schemes for the convective-diffusion discrete equations,in which the viscous and convection terms are discreted respectively as second-order center and QUICK scheme,are developed by using the numerical perturbation algorithm presented by Professor Gao Zhi. The reconstruction methods include the global reconstruction using all node-information in a discrete element, up-stream and down- stream reconstruction using upstream and downstream node-information,respectively. By using those two reconstructions,two kinds of numerical perturbation higher-order accurate schemes are obtained and called as Gao＇s QUICK scheme（G-QUICK scheme）.Simplicity of G-QUICK scheme is the same as QUICK scheme. Gao＇s algorithm was early used to reconstruct three node schemes of the convective-diffusion equations. The research in this paper shows that,Gao＇s algorithm is also effective for reconstruction of multi-node scheme like QUICK scheme.Compared with QUICK scheme,G-QUICK schemes for global reconstruction,up-stream and down-stream reconstructions,have the higher order accurate and wider stable region.For global reconstruction, G-QUICK schemes and QUICK scheme are conditionally stability;however for the up- and down- stream reconstruction,G-QUICK schemes contain some absolutely steady schemes.Excellent properties of G-QUICK schemes are proved by analysis and numerical tests.The G-QUICK schemes of up- and down- stream reconstruction provide a new way for QUICK scheme without artificial viscosity.Multi-node high order accuracy upwind and central schemes have been widely used in the calculation of turbulent.New schemes developed in this paper have the same high order accuracy but the less node,and their advantages and effectiveness in calculation of turbulent are worthy of further study.
出处
《力学学报》
EI
CSCD
北大核心
2011年第1期55-62,共8页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金(10872204)
教育部博士点基金(20070530003)资助项目~~
