Shearingbox-implementation for the central-upwind, constraint-transport MHD-code NIRVANA

We describe the implementation of the shearingbox approach into the Godunov-type central-upwind/constraint-transport magnetohydrodynamics code NIRVANA. This will allow for applications which require sheared-periodic boundary conditions as typically used in local Cartesian simulations of differentially rotating systems. We present the algorithm in detail and discuss necessary modifications in the numerical fluxes in order to preserve conserved quantities and to fulfill other analytical constraints as good as seem feasible within the numerical scheme. We check the source terms which come with the shearingbox formulation by investigating the conservation of the epicyclic mode energy. We also perform more realistic simulations of the magneto-rotational instability with initial zero-net-flux vertical magnetic field and compare the obtained stresses and energetics with previous non-conservative results exploring the same parameter regime.