We introduce a computational method for embedding Lagrangian sink particles into an Eulerian calculation. Simulations of gravitational collapse generally produce regions whose density greatly exceeds the mean density in the simulation. These dense regions require extremely small time steps to maintain numerical stability. Smoothed particle hydrodynamics (SPH) codes approach this problem by introducing non-gaseous, accreting sink particles, and Eulerian codes may introduce fixed sink cells. However, until now there has been no approach that allows Eulerian codes to follow accretion onto multiple, moving objects; we have removed that limitation. We have tested this new method and found that it produces excellent agreement with analytic solutions.
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