A treatment of discontinuities for finite difference methods (Q1206580)

A new version of the treatment of discontinuities in a hyperbolic system of conservation laws is developed. It is a variant of \textit{A. Harten's} \(x-t\) version [J. Comput. Phys. 83, 148-184 (1989; Zbl 0696.65078)]. This new version tracks discontinuity positions while the \(x-t\) version tracks the local conservation errors. The equivalence of these two versions is shown, provided the solution is piecewise smooth. Numerical experiments show that the author's treatment can be used efficiently in a two-step scheme and the results are qualitatively the same as in applying the \(x-t\) version of one-step schemes.