In this research a one-fluid method based on an exact Riemann solver with a novel wave pattern is presented. This model utilizes the isothermal equation of state which is consistent with the behavior of water in compressible fluid flow. The equation is a triple function and is able to capture the behavior of water in all liquid, two-phase and vapor phases. The Tait equation of state is used for the liquid phase and the pressure in the saturation dome is considered as constant saturation pressure P sat . The ideal gas equation of state is also used for the vapor phase. The present model assumes that the vaporization occurs via a distinct wave named as evaporation wave. The speed of the evaporation wave is considered as the last expansion wave in liquid phase. Because the pressure in saturation dome is constant, no wave can propagate in the two-phase region and the expansion wave only propagate in the liquid and vapor phases. Hence, a constant zone separates the general expansion wave into two different parts. The new model is verified with different 1D and 2D examples. First, a 1D shock tube problem with several initial conditions is simulated and the results are compared with the one-phase Riemann solver and modified-Schmidt model. Then the one-dimensional water hammer problem with cavitation is simulated and the results are validated with the experimental results. After that, the two dimensional underwater explosion problem is simulated and the results are compared with two different numerical simulations in the literature. The simulation is conducted using the Arbitrary-Lagrangian-Eulerian (ALE) scheme and the one-fluid method. In the ALE scheme, the interface of the gas bubble and the water medium moves Lagrangian and the other computational nodes moves arbitrarily according to the smoothing function and proportional to the interface movement. The triangular computational cell is implemented using the Delaunay triangulation method. In order to capture the wave front precisely, the adaptive grid with remeshing process is implemented in the ALE code. Then, the new method is used for simulation of supercavitating flow around different objects. First, the supercavitation phenomenon around the cylinder is explored and the effect of the cavitator head shape and the velocity of the free stream over the cylinder is studied and the cavitation bubble profile is compared with the other numerical and analytical solutions. Then, the supercavitating flow over the projectile is simulated. Results show a good agreement with other numerical and experimental results. In addition, the simulat ed results illustrates that the supercavitation flow cause significant reduction in skin friction drag and the total drag on the body is reduced. Keywords: Riemann solver, cavitation, One-fluid method, Equation of state, Compressible flow, Underwater explosion, Supercavitation