A TREATMENT OF DISCONTINUITIES IN SHOCK-CAPTURING FINITE-DIFFERENCE METHODS

In this paper a treatment to sharpen discontinuities for shock capturing methods is introduced. The treatment is a modification of the underlying scheme that makes the computation on each side of the discontinuity use information only from that side. The modification is done by adding specific artifical terms to the underlying scheme. The correctness of the discontinuity's location is guaranteed by some limitation of the artificial terms. Shock tracking ideas are involved in the treatment; however, no lower dimensional grid is needed to fit the discontinuity. A high resolution technique is set up to find out the location of the discontinuity within the cell. Several numerical examples including spontaneous shocks, linear discontinuity calculations, and the blast waves problem are presented. © 1991.