Block structured adaptive mesh and time refinement for hybrid, hyperbolic plus N-body systems

We present a new numerical algorithm for the solution of coupled collisional and collisionless systems, based on the block structured adaptive mesh and time refinement strategy (AMR). We describe the issues associated with the discretization of the system equations and the synchronization of the numerical solution on the hierarchy of grid levels. We implement a code based on a higher order, conservative and directionally unsplit Godunov's method for hydrodynamics; symmetric, time centered modified symplectic scheme for collisionless component; and a multilevel, multigrid relaxation algorithm for the elliptic equation coupling the two components. Numerical results that illustrate the accuracy of the cod and the relative merit of various implemented schemes are also presented. (C) 2007 Published by Elsevier Inc.