PIERNIK mhd code - a multi-fluid, non-ideal extension of the   relaxing-TVD scheme (I)
  We present a new multi-fluid, grid MHD code PIERNIK, which is based on the Relaxing TVD scheme. The original scheme has been extended by an addition of dynamically independent, but interacting fluids: dust and a diffusive cosmic ray 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, and a selfgravity module, Ohmic resistivity module, as well as other facilities which are useful in astrophysical fluid-dynamical simulations. The code is parallelized by means of the MPI library. In this paper we shortly introduce basic elements of the Relaxing TVD MHD algorithm, following Trac & Pen (2003) and Pen et al. (2003), and then focus on the conservative implementation of the shearing box model, constructed with the aid of the Masset's (2000) method. We present results of a test example of a formation of a gravitationally bounded object (planet) in a self-gravitating and differentially rotating fluid. 
Micha{\l} Hanasz, Kacper Kowalik, Dominik W\'olta\'nski and Rafa{\l}   Paw{\l}aszek