Two-dimensional interaction of Riemann compression waves

A class of solutions of the gas-dynamics equations containing a function ar bitrariness is used for a qualitative and quantitative analysis of the gas flow which occurs as a result of the interaction between Riemann compressio n waves. Two types of flow are investigated matched flow, when the adiabati c exponent is matched in a special way with the initial geometry of the com pressed volume, and the general case when there is no such matching. For ma tched interaction of non-self-similar Riemann waves, a phenomenon of partia l collapse is established (only part of the initial mass of the gas is comp ressed to a point); here the asymptotic estimates for the velocity, density , internal energy and optical thickness are the same as for self-similar co mpression. It is proved that unmatched interaction of self-similar Riemann waves does not lead to unlimited unshocked compression of the gas; in this case a shock wave occurs when the maximum density of the gas is finite. The results obtained enable us to say that two-dimensional processes of unlimi ted compression are stable for a fairly wide range of perturbations. (C) 19 99 Elsevier Science Ltd. All rights reserved.