Application of Molecular Hydrodynamics to Astrophysical Flows — Bondi-Hoyle-Lyttleton Accretion Flow —

The direct simulation Monte Carlo (DSMC) method, originally developed to treat rarefied gas dynamical problems, is modified to calculate continum gas flows. We do this by fixing the mean free path of simulated molecules in such a way that the continum properties of the fluid are maintained everywhere. We extend the scheme to take into account internal degrees of freedom, allowing us to treat arbitrary polytropic (γ) flows. The method can treat shock waves automatically without encountering the numerical oscillations that occur in non-TVD schemes. For this reason, the present method should not be considered of the DSMC type; instead it belongs to its own class of CFD methods, which we call 'molecular hydrodynamics' (MH). Using this method, we first calculate a plane Couette flow to estimate the magnitude of viscosity. Then we test the code for a one-dimensional shock tube problem. We demonstrate that we can obtain stable and reasonable solutions even if the time step is longer than that given by a Courant condition. Next, we test the two-dimensional step flow. In both cases, we assume γ = 1.4. As more realistic examples, we compute the two- and three-dimensional Bondi-Hoyle-Lyttleton accretion flow, and we demonstrate that the MH method can handle flows with infinite Mach number. The advantages of the MH are its robustness, its capability of handling flows of infinite Mach number, and its capability of treating vacuums/surfaces. A disadvantage of the MH is the rather large statistical fluctuations of its solutions.