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On a conservative finite-difference method for 1D shallow water flows based on regularized equations

P. 3-18.
Zlotnik Alexander, Gavrilin Vladimir.

We deal with the 1d shallow water system of equations and exploit its special parabolic regularization satisfying the energy balance law. We construct a three-point symmetric in space discretization such that the discrete energy balance law holds and check that it is well-balanced. The results of numerical experiments for the associated explicit finite-difference scheme are also given for several known tests to confirm its reliability and some advantages. The practical error behavior is also analyzed.

В книге

Под науч. редакцией: A. Batkai, P. Csomós, I. Faragó et al. Vol. 24. Berlin: Springer, 2016.