A TREATMENT OF DISCONTINUITIES FOR FINITE-DIFFERENCE METHODS IN THE 2-DIMENSIONAL CASE

This paper extends the treatment of discontinuities introduced by the author in [13], [14], and [15] to the two dimensional case. The main idea relies on the fact that on each side of a discontinuity the computations draw information from the same side. A numerical method for ordinary differential equations modeling the movement of the discontinuity curve is incorporated into the algorithm to compute discontinuity positions. The conservation feature of the treatment is studied for the case of an isolated discontinuity. Finally, we study two-dimensional scalar systems and systems of conservation laws and display some numerical results when our treatment is applied. © 1993 Academic Press. All rights reserved.