激波捕捉差分方法研究

在迎风型格式和矢通量分裂技术的基础之上，对捕捉激波方法进行一种新的尝试．该方法首先对原始格式在特征方向上进行投影，然后用限制器对这些特征分量的变化幅值进行限制以抑止非物理波动，最后再把它转换成守恒形式，得到了基本上无振荡的激波捕捉格式．用该方法对两种迎风显示格式(二阶和三阶)和3种迎风紧致格式(三阶、五阶和七阶)进行处理，并在一维和二维的情况下进行了应用测试．通过与高阶WENO、MP、Compact-WENO等格式的比较，表明该方法在光滑捕捉激波的前提下仍有较高精度和分辨率．

Developing Shock-Capturing Difference Methods

A new shock-capturing method was proposed which is based on upwind schemes and flux-vector splittings.Firstly,original upwind schemes were projected along characteristic directions.Secondly,the amplitudes of the characteristic decompositions were carefully controlled by limiters to prevent non-physical oscillations.Lastly,the schemes were converted into conservative forms and the oscillation-free shock-capturing schemes were acquired.Two explicit upwind schemes(2nd-order and 3rd-order) and three compact upwind schemes(3rd-order,5th-order and 7th-order) were modified by the method for hyperbolic systems and the modified schemes were checked on several one-dimensional and two-dimensional test cases.Some numerical solutions of the schemes were compared with those of a WENO scheme and an MP scheme as well as a compact-WENO scheme.The results show that the method with high order accuracy and high resolutions can capture shock waves smoothly.