BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//NA-M-81-13
       ENTRY:: January 28, 1996
ORGANIZATION:: Stanford University, Department of Computer Science, Numerical
               Analysis Project
       TITLE:: Large time step shock-capturing techniques for scalar
               conservation laws
        TYPE:: Manuscript
      AUTHOR:: LeVeque, Randall J.
        DATE:: July 1981
       PAGES:: 24
    ABSTRACT:: For a scalar conservation law $u_t\ = {f(u)}_x\ with f"$ of
               constant sign, the first order upwind difference scheme is a
               special case of Godonov's method. The method is equivalent to
               solving a sequence of Riemann problems at each step and
               averaging the resulting solution over each cell in order to
               obtain the numerical solution at the next time level. The
               difference scheme is stable (and the solutions to the
               associated sequence of Riemann problems do not interact)
               provided the Courant number $\nu$ is less than 1. By allowing
               and explicitly handling such interactions, it is possible to
               obtain a generalized method which is stable for $\nu$ much
               larger than 1. In many cases the resulting solution is
               considerably more accurate than solutions obtained by other
               numerical methods. In particular, shocks can be correctly
               computed with virtually no smearing. The generalized method
               is rather unorthodox and still has some problems associated
               with it. Nonetheless, preliminary results are quite
               encouraging.
       NOTES:: [Adminitrivia V1/Prg/19960128]
         END:: STAN//NA-M-81-13