A geometric approach to high resolution TVD schemes
by J. B. Goodman and R. J. LeVeque SIAM J. Numer. Anal. 25(1988), pp. 268-284.

Abstract. We use a geometric approach, similar to van Leers MUSCL schemes, to construct a secondorder accurate generalization of Godunovs method for solving scalar conservation laws. By making suitable approximations we obtain a scheme which is easy to implement and total variation diminishing. We also investigate the entropy condition from the standpoint of the spreading of rarefaction waves. For Godunovs method we obtain quantitative information on the rate of spreading which explains the kinks in rarefaction waves often observed at the sonic point.

pdf file

bibtex entry:

@Article{go-le:geometric,
  author =       "J. B. Goodman and R. J. LeVeque",
  title =        "A geometric approach to high resolution {TVD}
                 schemes",
  journal =      sinum,
  volume =       "25",
  year =         "1988",
  pages =        "268--284",
}