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One of the computational challenges of cluster formation simulations isresolving individual stars and simulating massive clusters with masses of morethan $10^4 M_{\odot}$ without gravitational softening. Combining direct$N$-body code with smoothed-particle hydrodynamics (SPH) code, we havedeveloped a new code, \textsc{ASURA+BRIDGE}, in which we can integrate stellarparticles without softening. We add a feedback model for \HII regions into thiscode, in which thermal and momentum feedback is given within the Str{\"o}mgrenradius. We perform $N$-body/SPH simulations of star cluster formation. Withoutsoftening, a portion of massive stars are ejected from the forming clusters. Asa result, the stellar feedback works outside the clusters. Thisenhances/suppresses the star formation in initially sub-virial/super-virialclouds. We find that the formed star clusters are denser than currentlyobserved open clusters, but the mass--density relation is consistent with oreven higher than that is estimated as an initial cluster density. We also findthat some clusters have multiple peaks in their stellar age distribution as aconsequence of their hierarchical formation.

SIRIUS Project. III. Star-by-star simulations of star cluster formation using a direct N-body integrator with stellar feedback