Piernik Mhd Code — a Multi–fluid, Non–ideal Extension of the Relaxing–tvd Scheme (ii)

We present a new multi–fluid, grid MHD code PIERNIK, which is based on the Relaxing TVD scheme (Jin and 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 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 introduce the multifluid extension of Relaxing TVD 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 gas pressure distribution. 1 Multifluid extension of the Relaxing TVD scheme The basic set of conservative MHD equations (see Paper I, (Hanasz et al., 2008), this volume) describes a single fluid. The Relaxing TVD scheme by Pen, Arras & Wong (2003) can be easily extended for multiple fluids by concatenation of the vectors of conservative variables for different fluids u = ( ρi,mix,m i y,m i z, e i } {{ } ionized gas , ρn,mnx ,m n y ,m n z , e n } {{ } neutral gas , ρd,mdx,m d y,m d z } {{ } dust ) , (1.1) 1 Toruń Centre for Astronomy, Nicolaus Copernicus University, Toruń, Poland; e-mail: [email protected] 2 School of Physics, University of Exeter, United Kingdom; e-mail: [email protected] c © EDP Sciences 2008 DOI: (will be inserted later) 2 Title : will be set by the publisher representing ionized gas, neutral gas, as well as dust treated as a pressureless fluid. In a short notation this can be written as