Features of the numerical solution of gasdynamic problems with many interacting discontinuities

An analysis is presented of difficulties associated with the numerical solution of hyperbolic problems of gas dynamics with many interacting discontinuities. Two model problems, the two-dimensional steady one and the one-dimensional unsteady one, are considered in detail. It is shown that if, special measures are not taken to improve the solution in the case of many discontinuities, dissipative schemes of both first and second order yield results that deviate significantly from results obtained on the basis of numerical schemes without dissipative properties. Attention is given to the efficiency of various procedures for the monotonization of the solution in conjunction with Abbett's (1971) procedure and various formulations of boundary conditions for the one-dimensional unsteady problem.