关于建立高阶差分格式的问题

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 式进行数值模拟。为能抑制计算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。

On the Construction of High Order Accuracy Difference Schemes

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.