Streaming instability in the quasi-global protoplanetary discs

We investigate streaming instability using two-fluid approximation (neutral gas and dust) in a quasi-global, unstratified protoplanetary disc, with the help of PIERNIK code. We compare amplification rate of the eigenmode in numerical simulations, with the corresponding growth resulting from the linear stability analysis of full system of Euler's equation including aerodynamic drag. Following Youdin & Goodman (2005), we show that (1) rapid dust clumping occurs due to the difference in azimuthal velocities of gas and dust, coupled by the drag force, (2) initial density perturbations are amplified by several orders of magnitude. We demonstrate that the multifluid extension of the simple and efficient Relaxing TVD scheme, implemented in PIERNIK, leads to results, which are compatible with those obtained with other methods.