We present a new multi-fluid, grid-based magnetohydrodynamics (MHD) code PIERNIK, which is based on theRelaxing 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 ofdynamically independent, but interacting fluids: dust and a diffusive cosmic ray (CR)gas, described within the fluid approximation, with an option to add otherfluids in an easy way. The code has been equipped with shearing-box boundaryconditions, a selfgravity module, an Ohmic resistivity module, as well as otherfacilities which are useful in astrophysical fluid-dynamical simulations. Thecode is parallelized by means of an MPI library. In this paper weintroduce a multifluid extension of the RTVD scheme and present a test caseof dust migration in a two-fluid disk composed of gas and dust. We demonstratethat due to the difference in azimuthal velocities of gas and dust and the drag force acting on both components, dust drifts towardsmaxima of the gas pressure distribution.