一种守恒型间断跟踪法用于处理一维Euler方程组中的若干问题  

DEALING WITH SOME PROBLEMS FOR EULER SYSTEM IN ONE SPACE DIMENSION IN A CONSERVATIVE FRONT-TRACKING METHOD

作　　者：刘妍[1] 茅德康[2] 

机构地区：[1]北京应用物理与计算数学研究所北京8009信箱16分箱,北京100088 [2]上海大学数学系,上海200436

出　　处：《高等学校计算数学学报》2006年第4期307-317,共11页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(10171063)资助.

摘　　要：1引言 间断跟踪法（front-tracking）是数值求解双曲型守恒型方程（组）的一种重要的数值方法，其主要特点是把间断作为移动的内边界来处理，光滑区域中的数值解用计算光滑解有效的数值方法来求解，而间断的移动和间断两侧的数值解的修正要满足Rankine-Hugoniot条件．我们称这样的跟踪法为传统的间断跟踪法（见[3]，[14]）．A conservative front-tracking method has been developed in [11],[12]. Unlike other front-tracking method, it advances discontinuities by enforcing the conservation properties of solution rather than the Rankine-Hugoniot condition. In this paper, we apply our front-tracking method to the Euler system of gas dynamics in one space dimension, in which shock reflection on solid walls is treated, spontaneous shock are captured and then tracked, and multifluid are concerned. The numerical examples in section 4 show the efficiency of our method in dealing with these problems.

关 键 词：间断跟踪法 守恒型方程 EULER方程组 一维 数值方法 数值求解 光滑解 数值解 

分 类 号：O175.2[理学—数学]