Interaction between a shock and an acceleration wave in a perfect gas for increasing shock strength

We study the interaction between a shock and an acceleration wave in an Euler fluid satisfying the ideal gas law, following the general theory developed by Boillat and Ruggeri [G. Boillat, T. Ruggeri, Reflection and transmission of discontinuity waves through a shock wave. General theory including also the case of characteristic shocks, Proc. Roy. Soc. Edinburgh 83A (1979) 17–24]. Special attention is devoted to analyzing the effects of varying the shock strength on the jump in the shock acceleration and on the amplitudes of the reflected and/or transmitted waves, for both weak and strong shock conditions. Our analysis confirms that, for a weak shock, the jump in the shock acceleration vanishes only when the incident wave belongs to the same family as the shock. Numerical calculations have also been performed and the numerical results are in perfect agreement with those obtained by application of the theory. Moreover, the numerical results, at variance with the theory, allow to gather information about the evolution of the solution after the impact time. 2007 Elsevier B.V. All rights reserved