Self-gravitational adaptive mesh magnetohydrodynamics with the NIRVANA code

I present a new version of the NIRVANA code capable for the simulation of multi-scale self-gravitational magnetohydrodynamics problems in three space dimensions employing the technique of adaptive mesh refinement. The building blocks of NIRVANA are (i) a fully conservative, divergence-free Godunov-type central scheme for the solution of the equations of magnetohydrodynamics; (ii) a block-structured mesh refinement algorithm which automatically adds and removes elementary grid blocks whenever necessary to achieve adequate resolution and; (iii) an adaptive mesh Poisson solver based on multigrid philosophy which incorporates the so-called elliptic matching condition to keep the gradient of the gravitational potential continous at fine/coarse mesh interfaces. In this paper I give an overview of the basic numerical ideas standing behind NIRVANA and apply the code to the problem of protostellar core collaps and fragmentation.