Numerous astrophysical phenomena have been studied by numerical simulations. As computing power increases such as parallel computing, it is now possible to perform high-resolution multi-dimensional hydrodynamics simulations with additional physics such as radiation and reaction. In this presentation, I briefly review numerical algorithms which incorporate the additional physics into the hydrodynamics code. For the astrophysical applications, there are three interesting reactions, nuclear, atomic, and molecular. Some example studies that include these three reactions are given in this presentation.