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We present an asymptotically and unconditionally stable numerical method toaccount for the momentum transfer between multiple species. Momentum isconserved to machine precision. This implies that the asymptotic equilibriumcorresponds to the velocity of the center of mass. Aimed at studying dustdynamics, we implement this numerical method in the publicly available codeFARGO3D. To validate our implementation, we develop a test suite for anarbitrary number of species, based on analytical or exact solutions of problemsrelated to perfect damping, damped sound waves, shocks, local and globalgas-dust radial drift in a disk and, linear streaming instability. Inparticular, we obtain first-order, steady-state solutions for the radial driftof multiple dust species in protoplanetary disks, in which the pressuregradient is not necessarily small. We additionally present non-linearshearing-box simulations of the streaming instability and compare them withprevious results obtained with Lagrangian particles. We successfully validateour implementation by recovering the solutions from the test suite to second-and first-order accuracy in space and time, respectively. From this, weconclude that our scheme is suitable, and very robust, to study theself-consistent dynamics of several fluids. In particular, it can be used forsolving the collisions between gas and dust in protoplanetary disks, with anydegree of coupling.

Asymptotically stable numerical method for multispecies momentum transfer: gas and multifluid-dust test suite and implementation in FARGO3D