Embedding Lagrangian Sink Particles in Eulerian Grids

We introduce a new computational method for embedding Lagrangian sinkparticles into an Eulerian calculation. Simulations of gravitational collapseor accretion generally produce regions whose density greatly exceeds the meandensity in the simulation. These dense regions require extremely small timesteps to maintain numerical stability. Smoothed particle hydrodynamics (SPH)codes approach this problem by introducing non-gaseous, accreting sinkparticles, and Eulerian codes may introduce fixed sink cells. However, untilnow there has been no approach that allows Eulerian codes to follow accretiononto multiple, moving objects. We have removed that limitation by extending thesink particle capability to Eulerian hydrodynamics codes. We have tested thisnew method and found that it produces excellent agreement with analyticsolutions. In analyzing our sink particle method, we present a method forevaluating the disk viscosity parameter $\alpha$ due to the numerical viscosityof a hydrodynamics code, and use it to compute $\alpha$ for our Cartesian AMRcode. We also present a simple application of this new method: studying thetransition from Bondi to Bondi-Hoyle accretion that occurs when a shock hits aparticle undergoing Bondi accretion.Comment: 35 pages, 10 figures. Submitted to Ap