Multi-scale simulations of black hole accretion in barred galaxies:
  Numerical methods and tests
  Due to the non-axisymmetric potential of the central bar, barred spiral
galaxies form, in addition to their characteristic arms and bar, a variety of
structures within the thin gas disk, like nuclear rings, inner spirals and
dust-lanes. In this first of two papers, we present a method to accurately
simulate the gas flow within the galactic plane in the 2D finite volume
software package FOSITE, which solves the transport equations for mass,
momentum and energy, and apply it to this class of objects. To this extent, we
introduced a new transport scheme for angular momentum and a very efficient
pseudo-spectral Poisson solver. Moreover, we provide a simple and generally
applicable method of how to take care of gravity in the energy equation.
