Abstract: 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.

Key words: cell-average, front tracking method, Riemann problem, discontinuity position