A TREATMENT OF DISCONTINUITIES FOR FINITE-DIFFERENCE METHODS

In this paper we develop a new version of the treatment of discontinuities developed earlier by this author. It is a variant of the x-t version in (J. Comput. Phys. 83, 148 (1989)). The new version differs from the x-t version in the sense that it tracks discontinuity positions instead of the local conservation errors. One of the main considerations of this paper is to show the equivalence between the two versions, by revealing the link between the discontinuity positions and the local conservation errors. In addition, a "stacking treatment" is developed to deal with discontinuities that locate in the same grid cell. Numerical experiments for applying the new version to a two-step scheme are presented, and the results are qualitatively the same as for applying the x-t version to one-step schemes. © 1992.