| Abstract
| - We present a new multi-fluid, grid-based magnetohydrodynamics (MHD) code PIERNIK, which is based on the Relaxing Total Variation Diminishing (RTVD) scheme. The original scheme 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 briefly introduce the basic elements of the RTVD MHD algorithm, following Trac & Pen (2003) and Pen et al. (2003), and then focus on a conservative implementation of the shearing-box model, constructed with the aid of Masset's (2000) method. We present the results of a test example of the formation of a gravitationally bound object (a planet) in a self-gravitating and differentially rotating fluid.
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