Long-range beam-beam interactions can cause significant degradation of beam quality and lifetime in high energy ring colliders. In this paper, we report on numerical simulation of the long-range beam-beam interactions at RHIC using a parallel strong-strong particle-in-cell code, BeamBeam3D. The simulation includes nonlinearities from both the beam-beam interactions and the arc sextupoles. Scan studies in tune space show strong emittance growth islands around 7th and 11th order resonances. The large emittance growth inside the resonance island is driven by the dynamic tune modulation together with the nonlinear forces from beam-beam interactions and sextupole magnet. The emittance growth decreases quickly as the beam-beam separation increases from four to six sigmas.