A shock tracking technique based on conservation in one space dimension

De-Kang Mao
In this paper, which i s a c o n tinuation of 20], 21], 22] and 24], we present a shock tracking technique in one space dimension. The main feature of the technique is that it uses the conservativity of the hyperbolic conservation laws rather than the Hugoniot condition to track discontinuities. Roughly speaking, the technique is as follows: The computation of a numerical solution on each side of a discontinuity uses information only from the same side. This can be done by employing
more » ... data on the same side. From the viewpoint of shock capturing the overall scheme is not conservative therefore, conservation errors that indicate how far the numerical solution is away from being conserved are formed on every time level. These conservation errors are used to locate the discontinuity positions within the grid cells. Numerical analysis of the conservation and of the relation between the conservation errors and discontinuity positions are presented. Handling of interactions of discontinuities is developed. Finally, n umerical examples are presented to show the e ciency of the technique.
doi:10.3929/ethz-a-004283832 fatcat:wyfwrbpnojco7kab2n66pp4iby