关于建立高阶差分格式的问题  

On the Construction of High Order Accuracy Difference Schemes

作　　者：张涵信[1] 李沁[1] 庄逢甘[2] 

机构地区：[1]中国空气动力研究与发展中心 [2]中国航天局

出　　处：《空气动力学学报》1998年第1期14-23,共10页Acta Aerodynamica Sinica

摘　　要：为了能在不太密的网格上捕捉到流场的细致结构，通常采用高阶精度的差分格式进行数值模拟。为能抑制计算过程中和在激波附近产生的虚假波动，本文从物理构思出发，提出了建立高阶格式的两个基本原则，作者称之为抑制波动的原则和稳定性原则。通过对典型问题的计算表明，这些原则是有效的，由此建立的二阶格式即ＮＮＤ格式无虚假波动，由此建立的三、四阶以上的格式仅在激波附近有微小波动。算例还表明，不符合文中原则的高阶格式的结果则要差得多。为了进一步克服激波附近的微小波动，文中还建议了两种方法，一种是基于熵增原则的方法，另一种是采用激波附近为二阶ＮＮＤ格式、其它区域为高阶格式的混合方法。In order to capture the subtle structure in the flow field using not too dense grids, the high order accuracy difference schemes are often adopted in numerical simulations. To suppress the virtual oscillations in computations and in the vicinity of shock waves, two basic principles are presented from the physical consideration, i,e., the principle of suppressing oscillations and the principle of the stability. Through the computations about some typical problems, these principles are found to be efficient. Based on the principles, the second order NND scheme are free of oscillations, the third, fourth and higher order schemes are only of tiny oscillations in the region of shock wave, and the schemes not obeying the principles in the paper give worse results. Moreover, to overcome the tiny oscillations in the vicinity of shock waves, two suggestions are proposed, one is the methods based on the principle of entropy increase, another is the mixing method, i.e., the scheme degenerates into the second order NND scheme in the region of shock wave and retains its high order accuracy in the rest of the field.

关 键 词：高阶精度 差分格式 计算空气动力学 混合格式 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程] O241.3[理学—计算数学]