Two-dimensional interaction of riemann compression waves

✍ Scribed by V.A. Kukushkin

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 787 KB
• Volume: 63
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(99)00053-2

✦ Synopsis

A class of solutions of the gas-dynamics equations containing a function arbitrariness is used for a qualitative and quantitative analysis of the gas flow which occurs as a result of the interaction between Riemann compression waves. Two types of flow are investigated matched flow, when the adiabatic exponent is matched in a special way with the initial geometry of the compressed volume, and the general case when there is no such matching. For matched interaction of non-self-similar Riemann waves, a phenomenon of partial collapse is established (only part of the initial mass of the gas is compressed to a point); here the asymptotic estimates for the velocity, density, internal energy and optical thickness are the same as for self-similar compression. 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 unlimited compression are stable for a fairly wide range of perturbations.