一种强健的守恒型间断跟踪法在一维Euler方程组上的实现

A Robust Front-tracking Method Based on Conservation for Euler System in One Space Dimension

文[8,9]研究设计了一种守恒型的间断跟踪法,其主要特点是以解的守恒性作为跟踪的机制而不是像传统的间断跟踪法利用Rankine Hugoniot条件,将该跟踪法对一维Euler方程组进行实现.对一维单个守恒律凸流的实现见文[7].由于Euler方程组有3类特征线,信息沿每类特征线传播并相互穿透.如果仍然象单个守恒律那样间断两侧的数值解的计算只用到来自间断同侧的信息,则间断一侧的信息就不能传到间断的另一侧,而会堆积在间断附近.设计了一种几乎是二阶的按特征方式分离信息的方法,将堆积在间断附近的信息分离.而且按此思想可做成高阶方法.该方法中不仅用到了精确Riemann分解,还用到了Roe[12]的近似Riemann分解及各种插值和重构技巧.数值实验表明这样的处理是有效的.

A conservative front-tracking method^([8,9]) has been developed . The main feature of the method is that it uses the conservation property of the solution rather than the Hugoniot conditions to track discontinuities. The goal of this paper is to realize the method for the Euler system in an almost second order fashion. Euler system has three different kinds of characteristics, and waves propagate along the characteristics. Thus, to do the front-tracking, in the vicinity of the tracked discontinuities, it is necessary to spearate the waves in other characteristic fields from the tracked discontinuities and then distribute them to the solution on the two sides. An almost second order accurate wave separation procedure be designed, which can separate waves and then distribute them. Numerical examples show the effciency of the method.