求解Euler方程的高精度的空间──时间守恒格式

A HIGH RESOLUTION SMCE - TIME CONSERVATION SCHEME FOR SOLVING EULER EQUATIONS

空间－时间守恒（ＳＴＣ）格式是近年来发展出的一种计算格式，在现有的ＳＴＣ格式构造过程中，流动变量在解元中的分布都用其一阶Ｔａｙｌｏｒ展开式来表示。ＳＴＣ格式的精度与所采用的Ｔａｙｌｏｒ展开式的阶数有关。该文采用流动变量的二阶Ｔａｙｌｏｒ展开式来表示其在解元上的分布，构造出了求解一维Ｅｕｌｅｒ方程的ＳＴＣ格式。用该格式对几个问题进行了计算，将计算结果与精确解进行了比较，比较表明该格式有较高的精度。

The space-time conservation (STC) scheme has been developed in recent years. In the constructing processes of the existent STC schemes, the distribution of flow variables in a solution element is approximately expressed by their first-order Taylor's expansions. The accuracy of the STC scheme is related to the order of Taylor's expansions. In this paper, a high resolution STC scheme for solving 1-D Euler equations is constructed by employing the second-order Taylor's expansions of flow variables to express their distribution in a solution element. Several test problems are solved by this scheme, and the numerical results are compared with the exact solutions. Comparisons show that the scheme presented in this paper has high accuracy.