On some operator splitting schemes in gas-dynamics problems with heat conduction

This work treats the construction and investigation of the high resolution type difference schemes that involve different limiters such as minmod,van Leer,superbee and some others. All considered schemes are quasimonotonic and lead to appearance of non-monotonies in the shock wave front. There is a class of initial conditions such that TVD schemes applied result in considerable local discrepancies between solution profiles. In particular, these problems arise where an initial velocity jump and singularities in density and temperature profiles are present.While for a wide class of problems the superbee limiter is optimal, in the last case minmod may have an advantage. Nevertheless, using the smoothed initial conditions, at least on 2 cells, or taking into account viscosity as well as introducing additional numerical dissipation allows to effectively apply schemes with limiters for solution of physical problems.