Abstract This paper presents the application of a numerical method for gas dynamics to model supersonic flows in a gas continuous, two-fluid medium. Specifically, flows in the two-phase medium are modeled only as single-phase compressible flow in a fixed, complex, multidimensional geometry. Coupling effects involving liquid response to interfacial forces are neglected. The motivation for development stems from the desire to predict blast interaction with liquid blankets in Inertial Confinement Fusion reactors. The model uses a second-order extension of Godunov's finite difference method to solve Euler's time-dependent equations of gas dynamics. The method uses a uniform Cartesian grid and a simple method for treating complex boundary geometries. The algorithm uses operator splitting to solve gas dynamics in multiple dimensions. Results of several problems are qualitatively and quantitatively compared with previous work and experimental data.