Techniques to treat interaction of tracked discontinuities,such as "stack",in a one-dimensional front-tracking method based on conservation (conservative front-tracking method) are developed and described in details.A numerical example is presented to illustrate the efficiency of the techniques.

In our foregoing paper[8] we had designed a nonlinear conservative difference scheme of second-order Godunov type with piecewise-linear reconstruction,in which the slope of the reconstructed function in each grid cell can be computed by dissipating the entropy. Such a scheme satisfies the entropy condition,and computes not only numerical solution but also numerical entropy; thus, it is different from all former conservative schemes. A socalled entropy dissipator in the scheme, which dissipates the entropy in each grid cell in the computation, plays an important role in stabilizing the computation. The entropy dissipator designed in is quite complicated. In this paper, we numerically discuss why entropy must be dissipated and how much entropy should be dissipated. A new entropy dissipator, based on the second-order difference of the numerical solution is given. Numerical examples are presented to show how the entropy dissipator suppresses nonphysical oscillations near discontinuities.

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.