Implicit SPH drag and dusty gas dynamics

a multiphase flow such as gas and dust, the time step for numerical integration is controlled by the Courant condition, by the drag between the fluids, and by gravity. If the dust particles are sufficiently small the time step is determined by the drag. Since the primary effect of very large drag is to keep the fluids moving together, and the details of how this is achieved are not important when the drag is very large, it is desirable to treat the drag terms implicitly. For standard grid-based methods this is straightforward, but for particle methods like SPH it appears difficult because the drag appears in the form of pair interactions between particles, and any given particle can interact with similar to 40 neighbours. The idea exploited in this paper is to treat each pair interaction separately. The velocities of the two particles involved are updated implicitly, according to their pair interaction, and the initial velocities of these particles are then replaced by the new velocities. This process is repeated for each pair interaction. Two sweeps over the particles gives satisfactory convergence. In this paper the method is tested first by keeping just the drag terms, then including pressure and drag to test wave propagation, and finally including gravity to consider the fall of a layer of gas in an isothermal atmosphere. The results are in good agreement with theory. The basic idea of working with implicit pair interactions can be extended to other SPH problems. (C) 1997 Academic Press.