When pressurized water or vapor leaks from a failed heat transfer tube in a steam generator (SG) of sodium-cooled fast reactors, a high-velocity, high-temperature jet with sodium-water chemical reaction may cause wastage on the adjacent tubes. For safety assessment of the SG, a computational fluid dynamics code SERAPHIM, in which a compressible multicomponent multiphase flow with sodium-water chemical reaction is computed, has been developed. The original SERAPHIM code is based on the finite difference method. In this study, an unstructured mesh-based numerical method was developed and introduced into the SERAPHIM code to advance a numerical accuracy for a complex-shaped domain including multiple heat transfer tubes. The multiphase flow under the tube failure accident is calculated by the multifluid model considering compressibility. The governing equations are solved by the Highly Simplified Marker And Cell (HSMAC) method. The original HSMAC method was modified for compressible multiphase flows in the unstructured mesh. Validity of the unstructured mesh-based SERAPHIM code was investigated through the analysis of an underexpanded jet experiment, which is a key phenomenon in the tube failure accident. The calculated pressure profile showed good agreement with the experimental data. Numerical analysis of water vapor discharging into liquid sodium was also performed. The calculated behavior of the reacting jet agreed with the previous experimental knowledge. It was demonstrated that the proposed numerical method could be applicable to evaluation of the sodium-water reaction phenomenon.