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We present a new multi-fluid, grid MHD code PIERNIK, which is based on theRelaxing TVD scheme. The original scheme has been extended by an addition ofdynamically independent, but interacting fluids: dust and a diffusive cosmicray 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, and a selfgravity module, Ohmic resistivity module, as well asother facilities which are useful in astrophysical fluid-dynamical simulations.The code is parallelized by means of the MPI library. In this paper we shortlyintroduce basic elements of the Relaxing TVD MHD algorithm, following Trac &Pen (2003) and Pen et al. (2003), and then focus on the conservativeimplementation of the shearing box model, constructed with the aid of theMasset's (2000) method. We present results of a test example of a formation ofa gravitationally bounded object (planet) in a self-gravitating anddifferentially rotating fluid.

PIERNIK mhd code - a multi-fluid, non-ideal extension of the relaxing-TVD scheme (I)