## 4 Cavitation Flow over the Hemispherical Head Form
### Interface Boundary Condition  
As described in the previous section, interface boundary conditions are required for parallel computations based on multidomain methods, and are critical in terms of the overall accuracy of parallel computations. The types of interface boundary conditions depend on the associated multidomain methods, namely the number of overlapped grid points. Three types of interface boundary conditions, including linear interpolation, two-point overlapped methods, and four-point overlapped methods, are used. Figure 7 shows a magnified view of the grids that were used for the serial and parallel computations. In Figure 7a, the computation domain consists of a single domain used for the serial computation. The results obtained from the serial computation based on the single domain are used as the reference results by which the accuracy and efficiency of the parallel computations are assessed. The validity of the serial computation is confirmed by comparing its results with the measured data. In the other parallel computations, the computational domain consists of multi-subdomains. Figure 6: Computation domain and associated boundary conditions. Figure 7: Grids used for serial and parallel computations; (**a**) single domain, (**b**) linear interpolation, (**c**) two-point overlapped, (**d**) four-point overlapped. Figure 8 shows the distribution of the cavitation flow around the body in terms of the water volume fraction where AL = 1 and AL = 0 denote pure water and vapor, respectively. The overall distributions of cavitation in all of the cases are similar to each other, which confirms the validity of the parallel computations. However, the pressure distributions on the body are compared with the measured data to examine the effects of the interface boundary conditions in further detail. Figure 9 compares the distributions of the predicted mean pressure coefficients along the body surface. The data measured by [PERSON] et al. [19] is also provided to confirm the validity of the numerical results. Generally, good agreements are observed between the numerical and experimental results, although there are not enough measured points around the peak for stricter validation. However, the numerical predictions by [PERSON] et al. [17; 30] showed results similar to the present ones: the peak value is located more downstream in comparison to the experimental result. Figure 8: Contours of water volume fraction at \(\mathrm{t}^{\bullet}\) = 30; (**a**) single domain, (**b**) linear interpolation, (**c**) two-point overlapped, (**d**) four-point overlapped. However, all of the numerical results slightly overpredicted the cavity length when compared with the experimental results. The pressure in the cavity is lower than that of the surrounding fluid such that flow is induced inside the cavity, and this causes a re-entrance jet. The cavity length depends on the re-entrance flow, and this implies that the cavity length exhibits high unsteadiness and varies relative to the re-entrance jet phenomena. In all of the numerical simulations, the re-entrance flow occurs at the end of the cavity. The unsteadiness potentially leads to the observed difference between the numerical and the experimental results. As shown Figure 9, the mean pressure coefficient obtained from the numerical result based on the four-point overlapped method closely follows that of a single domain. The other numerical results obtained from parallel simulations based on the linear interpolation and two-point overlapped grids are slightly lower than those in the single domain. This is due to the difference in the interface boundary conditions that are associated with the number of overlapped points in the parallel simulations. The difference does not appear to be critical to the overall computational accuracy of the simple problem. However, it is not possible to infer the same for problems involving complex geometry. Therefore, as noted in the previous section, the four-point overlapped method is proposed to resolve the issue.