The interaction of shock waves with fluid interfaces

AbstractEnhanced resolution for the computation of the interaction of shock waves with fluid interfaces is achieved through a detailed mathematical analysis of 2-dimensional wave interactions produced during the collision of the waves. This computation is carried to late times, which are characterized by interface instability and chaotic mixing processes. Algorithms for incorporating the wave interaction analysis and the resulting bifurcation of front topology give an important extension of the front tracking method and are presented here. The mathematical analysis shows that the customary theory for oblique 2-dimensional wave interactions is equivalent to a 1-dimensional Riemann problem for steady (supersonic) flow. This analysis, known for polytropic gases, is extended here to a general equation of state. Moreover, the asymptotic limit of a small incident angle is analyzed to obtain a well-conditioned numerical algorithm. This limit is found to define a 1-dimensional unsteady Riemann problem