Dr. Shihong Liao (廖世鸿) is currently a Researcher at the National Astronomical Observatories, CAS (NAOC). He obtained his PhD from the Chinese University of Hong Kong, and subsequently conducted postdoctoral research at NAOC and the University of Helsinki, before joining NAOC as a faculty member in 2024. His research focuses on galaxy formation, supermassive black holes, and cosmological simulations.Supermassive black hole (SMBH) binaries within galaxy mergers are the primary target for upcoming low-frequency gravitational wave (GW) observatories. Understanding the coalescence process of SMBH binaries in a cosmological galaxy formation context is crucial for accurate GW predictions. However, traditional galaxy formation simulations (including IllustrisTNG, EAGLE, and COLIBRE, etc.) often merge SMBHs instantaneously at kpc or sub-kpc separation scales due to resolution limitations, leading to significant uncertainty in estimating SMBH coalescence time-scales and GW predictions. In this talk, I will introduce our new numerical tools (i.e., the KETJU code and RABBITS series simulations), which can simultaneously follow galaxy (hydro-)dynamics and resolve SMBH dynamics with post-Newtonian corrections down to the GW inspiral phase. These numerical simulations enable us to improve the estimation of the SMBH merger time-scales (especially in gas-rich galaxy mergers) and related GW predictions, and study the impact of SMBH binaries on galaxy properties.