We studied the propagation of acoustic and shock waves in bubbly fluids using the Front Tracking hydrodynamic simulation code FronTier for axisymmetric flows. We compared the simulation results with the theoretical predictions and the experimental data. The method was applied to an engineering problem on the mitigation of cavitation erosion in the container of the Spallation Neutron Source liquid mercury target. The simulation of the pressure wave in the container and the subsequent analysis on the collapse of the cavitation bubbles confirmed the effectiveness of the non-condensable gas bubble injection method on reducing cavitation damage.; Then we analyzed the interfacial dynamics of liquid-vapor phase transitions and the wave equations for immiscible thermal conductive fluids. The phase transition rate is associated by the kinetic theory with the deviation of the vapor pressure from the saturated pressure. Analytical solutions to the linearized equations have been explored. The adiabatic and the isothermal limits have been investigated for both the linearized and the nonlinear equations, for latter the method of travelling wave solutions has been used. The wave structure of the solution to the problem with Riemann data has been discussed.; We also implemented a numerical scheme for solving the Euler equations with thermal conduction and phase transitions in the frame of front tracking. Heat conduction has been added to the interior state update with second order accuracy. Phase boundary propagation has been handled according to the interfacial dynamics. A numerical technique has been introduced to account for the thermal layer thinner than a grid cell. The scheme has been validated, extended to multi-dimension, adapted for cylindrical and spherical symmetry, and applied to the simulation of condensing and cavitating processes.
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