可压缩气液两相界面流动广泛存在于自然界与工业工程领域，如超燃冲压发动机燃烧室、水力机械以及生物医疗工程等。典型可压缩气液两相界面流动涉及到强激波与大密度比两相界面的复杂时空演变过程，例如激波与液滴以及激波与气泡的相互作用，两相流体密度比达到了103量级，压力比达到105量级，这对高精度数值模拟研究提出了极大挑战。本文以激波与气液两相界面相互作用问题为研究对象，发展了针对强可压缩两相界面流动数值模拟的高精度算法，对不同强度激波与液滴的作用以及激波与气泡的作用过程开展了研究，阐释了激波与气液两相界面相互作用基本规律，揭示了液滴在激波作用下的动力学规律以及激波作用气泡溃灭及其诱导射流的物理机制。首先，对激波与气液两相流体界面相互作用规律开展了研究。结果表明，从空气中入射的激波在激波角超过临界角度时，反射形式会从常规反射向马赫反射转变。当入射激波角逐渐增加时，水中透射激波沿着两相界面的速度分量会逐渐超过入射激波速度分量，形成前导型透射激波，发生前导型透射激波的临界激波角随着入射激波强度的增加而增大。从水中入射的激波在激波角超过临界角度时，反射膨胀波与入射激波发生干涉使得入射激波向前弯曲发生非常规反射。理论分析获得了激波与气液两相界面相互作用的极线图谱以及相互作用后的界面偏转角、透射激波角以及透射激波强度等参数。进一步，对空气中激波与液滴相互作用的流动规律进行了研究。结果表明，剪切诱导夹带机制是液滴在高马赫数激波作用下破碎的主要机制。当入射激波强度足够大时，透射激波被下游界面反射形成膨胀波，这些膨胀波汇聚形成的极低负压区是液滴内部发生空化的物理机制。入射激波在穿过液滴之后，部分波面后的压力逐渐恢复，相应地激波恢复为平面形状。当液滴内部存在气泡时，入射激波马赫数越高，液滴内部气泡尺寸越大，激波作用后的液滴内部气泡溃灭形成的一次横向射流强度越高。最后，对激波与不同偏心率椭圆形气泡相互作用规律进行了研究。结果表明，气泡溃灭过程中流体射流形成的主要机制归结于气液两相界面在激波作用下的偏转、Richtmyer-Meshkov不稳定性和反射膨胀

Compressible gas-liquid two-phase flows widely exist in nature and industry, such as scramjet engine combustors, fluid machineries and bio-medical technologies. Typical compressible gas-liquid two-phase flows involve complex physical processes of strong shock waves interaction with two-phase interfaces, such as shock waves interaction with droplets and bubbles. The density ratio can reach up to 103 and the pressure ratio across the shock wave can reach up to 105, which propose a great challenge for high resolution numerical study. In the present thesis, the problem of shock interaction with gas-liquid two-phase interface is studied numerically, especially on shock wave interactions with liquid droplets or gas bubbles. Based on the developed high resolution numerical method, the regularity of shock interaction with gas-liquid two-phase interface is revealed in details. The dynamical processes of the droplet and physical mechanisms of bubble collapse are further illustrated. A high resolution numerical scheme for compressible two-phase flow is developed. Based on the classical 5th order WENO scheme, a new incremental WENO scheme is proposed for a wider range of accuracy with one 3-point stencil replaced by two 2-point stencils. The incremental WENO scheme is able to handle closely located discontinuities with less numerical dissipations and achieve optimal 5th order accuracy in the smooth region. The current numerical method is free of spurious oscillations near two-phase interfaces and performs good numerical stability.The regularities of shock waves interacting with the plannar air/water interface are studied. Based on the numerical results, it is observed that the reflection regularities of shock wave passing from air to water are similar to that of shock wave reflection on the solid surface, which include the regular reflection and Mach reflection. The transmitted shock wave in the water can be precursor shock wave or non-precursor shock wave based on the incident shock angle and intensity. The critical angle that leads to precursor transmitted shock wave increases with the incident shock intensity. The refraction of incident shock wave passing from water to air has two patterns: regular refraction and irregular reflection. While for the irregular reflection, the reflection wave is a non-centered rarefaction wave and it overtakes the incident shock wave, leading to a forward concave wave ahead of the transmitted shock wave. The polar diagrams after the shock refraction are completed analytically. The interface deflection angle and the intensity of the transmitted shock wave are derived.The interactions of shock wave with a single droplet in air are studied. The breakup mechanism of the droplet under the shock wave is mainly due to the shear induced entraiment induced by the shock impaction. The low negative pressure near the downstream pole inside the droplet, which is mainly due to the converging of the expansion wave, indicates the possibility of the cavitation. The incident shock wave will recover partially after passing through the droplet. The interaction of the shock wave with a droplet embedded with a bubble is also considered. The embedded bubble will collapse and the first transverse jet occurs by the impaction of transmitted shock wave in the droplet. The first transverse jet is stronger under higher incident shock intensity or with larger bubble radius.The interactions of shock wave with a single elliptic bubble in liquid medium are studied. The bubble will collapse after the impaction of the incident shock wave and the first transverse jet forms. The interface deflection, the Richtmyer-Meshkov instability and the non-uniform flow are accounted for the formation of the first transverse jet. The formation position of the first transverse jet depends on the eccentricity and orientation of the elliptic bubble. With the axisymmetry effects considered, the intensity of the first transverse jet will be stronger than that of planar two-dimensional case. For the three-dimensitonal bubble, under the same incident shock wave, the intensity of the first transverse jet of the rugby-like bubble is much stronger than that of the disk-like bubble.