Application of Molecular Hydrodynamics to Astrophysical Flows. II Unconditional Stability

We discuss the physical background of the molecular hydrodynamics method (MH), a new computational fluid dynamics (CFD) technique that we proposed recently, and further test it to simulate isothermal flows including those of zero temperature gas. The problems considered are a shock tube of an isothermal gas, a rotating cone test, a box shear flow test, and a Keplerian disc. We demonstrate that the MH is unconditionally stable in spite of the fact that the scheme is time-explicit. Because of this, we may choose any time step without losing stability. The only penalty for using a longer time step is a gradual degradation of the quality of the solution.