中文摘要：

对时-空守恒元解元算法（CE/SE）的网格设置做较大改进,提出一种新的六面体解元和元定义;同时在解元中对物理量进行高阶Taylor展开,给出一种在时间和空间上均具有高阶精度CE/SE算法.在此基础上,把新型的高阶精度CE/SE算法推广应用于高速流动捕捉激波间断、气相化学反应流动、计及固体动态效应的流体-弹塑性流动和非稳态多相不可压缩粘性流动中.数值实践表明,提出的新型网格结构上的高阶精度CE/SE算法具有算法简单、计算精度高、计算效率和计算效果好的优点,并大大改进和拓展了CE/SE算法的应用范围.

英文摘要：

Space-time conservation element and solution element （CE/SE） method with second order accuracy is modified on hexahedral grids. High-order accuracy in space and time is obtained by expanding variables in SEs with high order. CE/SE method is used to capture shock waves in chemical reaction flows, elastic-pLastic flows and unsteady multi-phase incompressible flows. Numerical results are compared with experimental and theoretical results of classical examples. It is indicated that the method is easy to implement, accurate and efficient. Application of high order CE/SE method is extended.