Use of TVD-schemes to simulate gasdynamic flows with spherical and cylindrical symmetry

A generalization of the Harten TVD-scheme in the form of a predictor-corrector-type scheme of second-order accuracy in time and space is proposed for the flows with spherical and cylindrical symmetry. The scheme does not require introducing components with artificial viscosity and describes discontinuities in the solution without the appearance of nonphysical oscillations for a Courant number less than 0.8.