A Hydrochemical Hybrid Code for Astrophysical Problems. I. Code Verification and Benchmarks for Photon-Dominated Region (PDR)

A two dimensional hydrochemical hybrid code, KM2, is constructed to deal with astrophysical problems that would require coupled hydrodynamical and chemical evolution. The code assumes axisymmetry in cylindrical coordinate system, and consists of two modules: a hydrodynamics module and a chemistry module. The hydrodynamics module solves hydrodynamics using a Godunov-type finite volume scheme and treats included chemical species as passively advected scalars. The chemistry module implicitly solves non-equilibrium chemistry and change of the energy due to thermal processes with transfer of external ultraviolet radiation. Self-shielding effects on photodissociation of CO and H$_2$ are included. In this introductory paper, the adopted numerical method is presented, along with code verifications using the hydrodynamics modules, and a benchmark on the chemistry module with reactions specific to a photon-dominated region (PDR). Finally, as an example of the expected capability, the hydrochemical evolution of a PDR is presented based on the PDR benchmark.