一种混合型四阶格式、基于特征的边界条件及其应用

A Hybrid Fourth Order Scheme and Boundary Conditions Based on Characteristics and Their Applications

本文描述并应用差分格式的构造原则 ,采用了时空转换的格式构造方法构造了一个四阶精度的差分格式 ,文中还进一步提出将四阶格式和二阶NND格式混合的方法 ,即在光滑区格式保持四阶精度、在激波附近降为二阶NND格式 ,来增强格式捕捉激波的能力。同时 ,本文基于特征传播的思想 ,建立了一种开边界的数值计算方法 ,并采用将边界条件嵌入控制方程的方法以及新的简化形式的边界处理方法 ,完整给出了无粘。

In this paper,the criteria about the construction of the difference schemes are recited and used to form a fourth order accuracy scheme combined with the temporal spatial transformation.Moreover,a hybrid scheme using the fourth order scheme and the second order NND scheme is also designed,i. e.,the scheme maintains the fourth order accuracy in the smooth region and changes into the second order NND scheme in the region of the shock wave.In the meanwhile,a kind of open boundary condition is constructed based on the idea of the characteristic propagation.Using the imbedded and simplified form of realization,the complete boundary processing methods including the inviscid boundary,viscous boundary and open boundary are presented.