Absorbing boundary conditions for astrophysical MHD simulations

Many problems for systems of conservation laws are formulated either on infinite domains or on domains which are by orders of magnitude larger than the interesting structures. In the first case, it is often impossible to find an exact representation of the problem which is suitable for numerical simulations. But even in the second case it can be difficult to perform the simulation on the whole domain, since much computational effort is wasted in uninteresting regions. Therefore the size of the computational domain has to be reduced, which introduces new boundaries without physical meaning. At these artificial boundaries suitable boundary conditions for the PDEs have to be formulated. In this paper we will discuss a method to derive artificial non-reflecting boundary conditions for systems of conservation laws. We will concentrate on the equations of ideal magnetohydrodynamics (MHD) in a gravitationally balanced, stratified atmosphere. We will state the main results, discuss implementational aspects and show results in 1D and in 2D.