###### Abstract
In the overlapping method, additional interface mesh points that are termed as dummy points are included in each subdomain. At the end of each numerical time integration step over each subdomain, data exchange between subdomains exchange occurs through overlapped points. The dependent variables on the interface boundary of each subdomain are updated using the data on the dummy points. However, to the best of authors' knowledge, there has been no systematic analysis on the accuracy of the domain decomposition methods. In the study, the accuracy of the domain decomposition methods is analyzed in combination of the alternating direction implicit (ADI) schemes. Based on the result, the overlapped multidomain method is proposed to be as accurate as the serial single-domain method. In addition, the efficient moving body-fitted overset grid technique is proposed, which can be combined with the background overlapped multidomains method to enable efficient and accurate parallel computations of complex two-phase flow problems involving complex moving foreign bodies. First, cavitation flow over a hemispherical head form is selected as a benchmark problem. The reason for the selection of the problem is two-fold: first, since the problem has been used for the validation of the related numerical methods in a lot of preceding studies, there are a lot of numerical data as well as the experimental data for comparison, and the other is that the final goal of the present development of numerical methods is to investigate the effects of incoming gust on cavitation flows around a high-speed submerged projectile. The current numerical methods based on the preconditioned dual-time stepping compressible Navier-Stokes (NS) equations solvers combined with the cavitation model on serial computation are validated by comparing the prediction results with the measured data. Subsequently, parallel computing techniques combined with the overlapping methods over multiblocks are applied. The validity of the proposed algorithms is confirmed by comparing the numerical results between the parallel computations using the overlapping methods and serial computation. Finally, multidomain methods are combined with the moving overset grid technique to simulate the gust flow generated by twin pitching hydrofoils. The moving body-fitted overset grids are used to model the oscillating hydrofoils, and the multiblocks with overlapping interfaces are used to model the background flow. The validity of the present numerical method is confirmed by comparing the numerical results with measured data. The governing equations and basic numerical methods are introduced in Section 2. The accuracy of the overlapped multidomain methods in combination with the ADI scheme are analyzed, and the overlapped method, which is as accurate as the corresponding single-domain method, is proposed in Section 3. The numerical results obtained from the serial computation of the cavitation flow over a hemispherical head form are presented and compared with the experimental data, and the parallel computation results obtained from the proposed multidomain methods with the overlapping interfaces are subsequently applied and validated in Section 4. The moving body-fitted overset grid methods consist of three sequential stages, including hole-cutting, finding donor cells, and interpolation, which are described in Section 5. Finally, the numerical results obtained from the application of the present numerical method based on the moving body-fitted overset grids combined with the background overlapped multidomains to the second benchmark problem, including the gust flow that is generated by twin pitching hydrofoils, are presented in terms of their comparison with the measured data in Section 6. The conclusions are detailed in Section 7.