We present a new multi-fluid, grid-based magnetohydrodynamics (MHD) code PIERNIK, which is based on the
Relaxing Total Variation Diminishing (RTVD) scheme (Jin & Xin 1995). The original scheme (see Trac & Pen 2003 and Pen et al. 2003) has been extended by an addition of
dynamically independent, but interacting fluids: dust and a diffusive cosmic ray (CR)
gas, described within the fluid approximation, with an option to add other
fluids in an easy way. The code has been equipped with shearing-box boundary
conditions, a selfgravity module, an Ohmic resistivity module, as well as other
facilities which are useful in astrophysical fluid-dynamical simulations. The
code is parallelized by means of an MPI library. In this paper we
introduce a multifluid extension of the RTVD scheme and present a test case
of dust migration in a two-fluid disk composed of gas and dust. We demonstrate
that due to the difference in azimuthal velocities of gas and dust and the drag force acting on both components, dust drifts towards
maxima of the gas pressure distribution.