We present an asymptotically and unconditionally stable numerical method to account for the momentum transfer between multiple species. Momentum is conserved to machine precision. This implies that the asymptotic equilibrium corresponds to the velocity of the center of mass. Aimed at studying dust dynamics, we implement this numerical method in the publicly available code FARGO3D. To validate our implementation, we develop a test suite for an arbitrary number of species, based on analytical or exact solutions of problems related to perfect damping, damped sound waves, shocks, local and global gas-dust radial drift in a disk, and linear streaming instability. In particular, we obtain first-order steady-state solutions for the radial drift of multiple dust species in protoplanetary disks (PPDs), in which the pressure gradient is not necessarily small. We additionally present nonlinear shearing-box simulations of the streaming instability and compare them with previous results obtained with Lagrangian particles. We successfully validate our implementation by recovering the solutions from the test suite to second- and first-order accuracy in space and time, respectively. From this, we conclude that our scheme is suitable, and very robust, to study the self-consistent dynamics of several fluids. In particular, it can be used for solving the collisions between gas and dust in PPDs, with any degree of coupling.
- circumstellar matter
- methods: numerical
- planets and satellites: formation
- protoplanetary disks