Modeling of one-dimensional shallow water flows based on regularized equations

For one-dimensional shallow water flows, a version of regularized equations deriving is expounded. The energy equality is proved for them. A corresponding finite-difference scheme is presented and examples of computation of one- dimensional problems known in literature are given encluding a disintegration of discontinuity (dam break) in a channel with a wall, subcritical, transcritical, supercritical flows over a hump, basins at rest, double rarefaction wave over a step, tidal flow over a beach and a disintegration of discontinuity in a horizontal and slanted dry bed channels. Convergence and exactness of the finite-difference scheme are analyzed.