Application of schemes based on the differential approximation method to invariant solutions in the gas sphere expansion into vacuum

This paper considers the problem of obtaining invariant solutions under rotation transformation in the expansion of a gas sphere into vacuum in the Cartesian coordinates for the two-dimensional case. Numerical results are presented and a comparative analysis of conventional and invariant difference schemes is made. Various non-invariant difference schemes of first and second approximation orders are considered. These results show that only the use of an invariant scheme constructed on the basis of the method of differential approximation allows obtaining a correct solution on uniform not dynamic coarse grids.