Simulating hydromagnetic processes in star formation: introducing ambipolar diffusion into an adaptive mesh refinement code

Given the importance of simulating hydromagnetic processes that impact star formation, we have earlier developed a 3D adaptive mesh approach that allows us to include hydromagnetic processes during the formation and evolution of cores, discs, and stars in observed regions of star formation. In this paper, we take the next step in this program - namely - to develop a modified version of the 3D adaptive mesh refinement (AMR) code FLASH in which the ambipolar diffusion of the magnetic field in poorly ionized molecular gas is implemented. We approach the problem using a single-fluid approximation to simplify numerical calculations. In this paper, we present a series of test cases including oblique isothermal and non--isothermal C-shocks. We also present a study of the quasi-static collapse of an initial uniform, self-gravitating, magnetized sphere that is initially supported by its magnetic field against collapse (i.e. magnetically subcritical). Applications to the collapse of a pre-stellar Bonnor-Ebert sphere are presented in a companion paper.