Singularities of numerical solution of gas-dynamical problems with many interacting discontinuities

Two-dimensional models of gas-dynamic problems with many interacting discontinuities are discussed. On the basis of a numerical experiment, the difficulties arising in constructing solutions of such problems by dissipative methods are demonstrated. A comparison of the corresponding calculations with the data of a numerical method without dissipative properties is given, and various means for improving the quality of the numerical results (in particular, at the boundary of the calculation region), obtained by the use of dissipative schemes are examined.