In this paper a numerical simulation of unsteady sheet cavitation is presented as it occurs on an NACA-0015 hydrofoil. The computational approach is based on the Euler equations for unsteady compressible flow, using an equilibrium cavitation model of Schnerr, Schmidt, and Saurel. It was found that for a computational method that directly uses the thermodynamic closure relations, more than 90% of the computational time was spent in computations associated with these relations. To circumvent this problem, the computationally costly method is replaced by using precomputed multiphase thermodynamic tables containing the same information, with no need to determine the flow phase. The thermodynamic computations using this approach are almost instantaneous. However, preparing these multiphase tables is not straightforward. The main difficulty is due to the slope discontinuities in the phase-transitioning regions of the multiphase tables. In these regions, the conventional look-up approaches are inaccurate and inefficient (their accuracy is insensitive to data grid refinement). To remove this bottleneck, phase-oriented interpolations in transition cells is developed as a novel approach that allows for preparing much more accurate and efficient (much smaller size) multiphase thermodynamic tables compared to conventional interpolation approaches.